Who would it be for each sport? This doesn't necessarily mean BYU would be able to sign them (so they'd still have to be a good fit for BYU), just that they would make them a prime target in recruiting.
Football: Jerry Rice. Having the best WR in football history added to the offenses from '81-'84 would've been even more unbelievable than it was.
Basketball: Stephen Curry. Curry would've been the perfect lead guard for Rice's system in Rose's early years. Oh, and Curry+Jimmer for 2 years? Yes please.
Both played at small schools so BYU would've had a good shot to sign them, and neither would seem to have issues with the HC.