Once a player attends one class after enrolling as a full-time student, he is considered officially enrolled as far as NCAA transfer rules go and as far as becoming a "counter" toward the scholarship and roster limits. Summer school before freshman year doesn't count. Basically, it's day one of the fall semester. That's when the school needs to be within the 11.7 scholarship limit and the 28 scholarship athlete limit.
The shorter draft signing window decreed by MLB's most recent collective bargaining window gives college coaches a lot more flexibility in reacting to the draft.
At the front end of the pipeline, coaches now know in early July which of their recruits will go pro. When my son was a freshman, the MLB signing deadline wasn't until mid-August. One of his new teammates, who had been drafted in the middle-rounds after telling every MLB team he was definitely going to college, attended summer school with him all summer. When he went home for the short break between summer school and the fall semester, the team that had drafted him offered him 4th round money. He took it, never went back to college and is in MLB now. His departure left the college coach with an unused hefty scholarship and no time to find a suitable place to invest that money.
At the back end of the pipeline, coaches now also know in early July which of the previous year's juniors and draft-eligible sophomores have gone pro. Returning players typically learn their status for the coming year at the end-of-season conference with their coach. If they're not part of next year's plan, they know it before they go home in May or June.
If coaches find themselves in an over-booked situation, they now have more than a month to "encourage" players outside the margins to pursue options more likely to serve their happiness. It does happen, but it happens less often than you might think, partly because coaches' livelihoods depend on their ability to manage the draft risk, and partly because so many players agree to funding packages that include no or minimal athletic money. There's a lot more merit and need-based money out there than athletic scholarship money. We seldom know the details of anyone else's deal, but when we do hear them, it's often surprising to hear how little baseball money some outstanding players actually receive.
As far as getting down to the 35 player roster limit, schools don't have to post their official squad list until a few days before the season starts in February. That means D1 schools can carry 40+ players all through fall practice. In that situation, the 28 scholarship counters are safe because their roster spots can't be given to anyone else, but the other 10 or 15 players go through the fall semester knowing they're competing for the remaining seven roster spots. Their situation is more precarious from a baseball perspective, but more secure from an education perspective because quitting or getting cut doesn't affect their financial ability to remain at school.
Regardless of the components of a player's aid package, the bursar's office at the school will require payment or firm commitments for the full cost of the player's tuition and fees before the semester starts.
Does this help?