Because the transferring player is on the team (he's a redshirt player) he still has to be enrolled in school, and if he's not on scholarship, he's essentially a walk-on, meaning he has to pay his own way. Redshirts in transfers seasons aren't some magical thing where a guy can join a team and not count against their scholarship limit, again, unless he's willing to pay his own way.
In Thompson's case, paying for school itself wouldn't be a problem in the least, but the idea that he'd come here for a year and pay his own way when plenty of other D1 schools would happily offer him a scholarship seems far-fetched. IMHO, Thompson will never suit up for the Gophers.
EDIT: Sorry to repeat. JWill's post must have gone up as I was typing my own.