The honest answer is in two parts and both matter.
Yes, these designs move the ball, and the mechanism is real. No, they do not change what your swing is doing, and the difference between those two sentences is what decides whether buying one is a good idea for you.
What causes a slice, briefly
Ball flight is governed by the club face's orientation at impact and the path the club is traveling on. In broad terms, the ball starts roughly where the face points and curves away from the path.
A slice for a right-handed golfer is a face that is open relative to the path through impact. That is the cause, and every equipment feature described below is aimed at that relationship.
The three mechanisms, and they are different
Manufacturers use several approaches and they are frequently bundled under one label.
Weight moved toward the heel. Shifting mass toward the heel side encourages the head to rotate closed through impact. This is the classic draw-bias design and it is what most draw-weighted drivers are doing.
A closed face angle. The face is built pointing slightly left of the target at address for a right-hander. This is the simplest approach and it is real, though it is also the one most visible to a golfer who dislikes how it looks at address.
Offset. The leading edge is set back behind the hosel. Common in irons and in some drivers. The stated effect is to give the hands fractionally more time to square the face, and it also raises launch by moving the center of gravity slightly further back.
Adjustable weighting, on drivers with a movable weight track, lets the golfer position mass toward the heel or the toe themselves. That is the same mechanism as the first, put under the owner's control.
These are separate features and a club can have one, some or all of them. A page describing a driver as draw-biased may mean any of them.
What they will and will not do
They will change the ball's curve, on average. The mechanisms are physical and they work. A driver weighted toward the heel produces less rightward curve for the same swing than the same head weighted toward the toe.
They will not change your face-to-path relationship. Your swing is unchanged. What has changed is the club's behavior within that swing.
They will not turn a large slice into a straight ball. The magnitude of correction available from any of these features is bounded by the amount of mass a designer can move and by the rules limits on the head. A curve produced by a substantially open face is larger than that.
They will not adapt. If your swing changes, whether through lessons or through a good month, the club keeps doing what it does. A golfer who fixes a slice and keeps a strongly draw-biased driver has traded one miss for the other one.
And they cannot be published as a number you can check. No maker publishes a yardage correction for a draw-biased model, because the figure would depend entirely on the swing applied to it. Any specific correction figure you encounter is describing one test with one golfer or one robot under one set of conditions, and this site publishes none.
The trade-offs nobody puts on the box
Weighting toward the heel is weight not spent elsewhere. The mass a designer uses to encourage face closure is mass not available to maximize resistance to twisting on off-center hits. There is a real, if modest, trade against resistance to twisting on off-center strikes, which this site covers separately under moment of inertia.
A closed face at address bothers some golfers enough to matter. If a club looks shut at address and you instinctively compensate, the feature has produced a swing change you did not want.
Offset in irons changes the look of the club at address, and preference here is strong and legitimate in both directions.
And it is one more thing tying you to a specific club. A club chosen to correct a fault is a purchase made about a temporary state.
The honest comparison
Three routes exist to a straighter tee shot and it is worth seeing them side by side, without a recommendation attached.
Equipment. Immediate, costs money, effect is bounded, does not adapt, and does not address the cause.
Instruction. Slower, costs money, addresses the cause, and the result is portable to every club in the bag.
Adjustment of what you already have. Free or nearly so. Many modern drivers have adjustable hosels and some have movable weights, and a golfer who has never moved either is leaving a real option unused. If yours is adjustable, that is worth a look before it is worth a purchase, and our article on what adjusting a driver mid-round means under the Rules covers the separate question of when you are allowed to change it.
Most golfers who ask this question have not tried the third one, which is the practical observation worth taking from this page.
What a fitting adds here
This is the one situation where a fitting answers the question directly rather than approximately.
A launch monitor measures your face-to-path relationship. That is the actual cause of the curve, expressed as a number, and it tells you whether the amount of correction available from a draw-biased head is meaningful against the size of your problem or not.
A golfer whose face is marginally open is a good candidate for the equipment route. One whose face is substantially open is buying a partial solution, and knowing which you are is worth more than any product comparison.
The one-line version
Draw bias, closed faces and offset move the ball. They do not move the swing. They are a real and bounded effect, they trade against other design properties, and they do not adapt when you improve.
Whether that trade is worth making is a decision about your own game, and it is a better decision made after measuring the cause than after reading a product page. Which is the same principle that runs through the rest of this cluster: our page on the golf club spec sheet, translated covers which of the numbers on a club are measurements and which are names.
FAQ
Does a draw bias driver actually work?
The mechanisms are physical and they do move the ball: a driver weighted toward the heel produces less rightward curve for the same swing than the same head weighted toward the toe. What it does not do is change the face-to-path relationship your swing produces.
Will a draw-biased driver fix a big slice?
No. The correction available is bounded by how much mass a designer can move and by the rules limits on the head, and a curve produced by a substantially open face is larger than that. It is a partial solution for a large slice.
What is offset, and how is it different from draw bias?
Offset sets the leading edge back behind the hosel. The stated effect is to give the hands fractionally more time to square the face, and it also raises launch by moving the center of gravity slightly further back. Heel weighting and a closed face angle are separate mechanisms, and a club can have one, some or all of them.
Are there downsides to a draw-biased driver?
The mass used to encourage face closure is not available to maximize resistance to twisting on off-center hits, a closed look at address bothers some golfers enough to cause an unwanted compensation, and the club does not adapt: fix the slice and you have traded one miss for the other.
Is there anything to try before buying one?
Yes. Many modern drivers have adjustable hosels and some have movable weights, and adjusting what you already own is free or nearly so. A launch monitor session also measures your face-to-path relationship, which tells you whether the bounded correction on offer is meaningful for your particular slice.