That's not too likely. In visual/graphic arts, that just isn't done.

They might buy his concept for the illustration, and have someone else develop it into a painting (which would be odd, they'd much more likely ask the new artist to illustrate the same scene in his own way), but they'll almost certainly won't have anyone finish the actual work done by Sweet (that would be something for the Sweet succession to agree to, and it's very unlikely an artist's succession would ever allow this).

If the sketch is in any state to be shown, it would be far more proper to nod to Sweet's contribution (if they feel it should be done, anyway. I couldn't care less personally) by including a b&w reproduction of his sketch in the book with a few words from Harriet about his work on the series and this planned last paintin, and to go for a different cover by a new artist.

Personally, I would not attempt to do one last cover in the vein of Sweet but done by someone else (I don't see the point of doing that personally, though I know a lot of people are very anal retentive when it comes to sets of books that have to match visually on their shelves and Harriet might well take this into account and favour a Sweet-style painting with the old layout for AMOL, even though in the case of Tor's edition of TWOT wishing to display them anywhere demonstrates about as much good taste as putting a series of clowns on black velvet on your walls. Even stripped of their tacky dust jackets those books still look bad),

I would rather go ahead now with the complete graphic makeover of the series which was alluded to for after the publication of the final book. Harriet wanted to keep the old design until then (unless something happened to Sweet in which case they would reconsider all this, Doherty and her pointed out at the panel- he was already quite sick back then), and when asked about it she answered she had no idea if they would go or not with the look and art created for the ebooks when the time came to revamp the books. With Sweet's passing, the purpose of finishing the series with the old look and his "distinctive style" is a bit moot. If they decided to use the ebooks' layout and art pieces for the revamp (which would make sense as they got fairly good reception from the fanbase), they have nearly a full year to gradually introduce the paperbacks with new art as their stock for each title runs out, and by next fall the fans would be used to the new look of the books.

Several publishers (incl. Tor) have done this in the past with series in progress (this happened with the Malazan books, notably - the books got a revamped look before the last novel came out, and the publisher started the ball rolling by introducing in stores the previous books of the series with the new look, as their printed stock of each title ran out).