This is (as has been pointed out above) perhaps the most contentious shot in pool as far as the rules are concerned.
As far as the rules are concerned, it's pretty clear. You can take any normal stroke through or partly into an object ball that's frozen to the cue ball. If you play almost directly at the ball and use follow, it's possible for the cue ball to pass the object ball as they go together down the table. By the current rules, that's perfectly legal. You are not required to jack up on the shot, and whether the cue ball slows with draw has no bearing on the legality of the shot.
As far as what's happening physically on the shot, there's a lot more information available now than there was 15 years ago due to the ultra-high-speed videos that have been made to study the shot. On frozen ball shots, there is only one tip-to-cue ball contact and you don't get a double hit. Whether that's true or not has little bearing on the rule, but it's nice to know that you aren't double-hitting the cue ball on such shots.
When faced with a nearly frozen situation, some players will jack up and get some draw to slow the cue ball down and claim a good stroke. Of course such shots are clearly fouls. Nearly frozen is treated in the rules as very, very different from frozen.