Yes. Much of the $$ will be for personal appearances. As to the question of whether players would be able use SLU logos, names, etc., it's an interesting topic. In some situations, top-tier players may compete with SLU for sponsorship dollars. In others, there may be joint team/player/sponsor opportunities. In yet other situations, sponsors may use player appearances as a cheap way to buy an implied relationship with SLU/team or defeat another sponsor's exclusivity. Each might have different solutions as to use of marks.
There may be some top-tier players who capture the entire market's passion who advertisers want for more than just appearances. They might compete with the school for sponsorship $$. Now if the sponsor also buys a team sponsorship (or if already a team sponsor,) would SLU prohibit the use of their trademarks and all of the resulting co-marketing opportunities simply because the player is also getting paid? I wouldn't.
Now if the sponsor is major, didn't buy a SLU sponsorship (bought the player only) -- and wants more than player appearances -- if you're SLU, you're probably prohibiting use of marks. But there are downsides: no SLU awareness via promotional co-marketing activities, and it reduces the opportunity to use this player-only sponsorship to ultimately bring the sponsor into a SLU sponsorship down the road. It also runs the possibility of angering your player if the deal goes south (because you didn't allow use of marks,) literally costing the player big money. Maybe the player walks at end of school year.
There are two other situations. 1) Some schools offer exclusive sponsorships within business categories. For example, "official beer sponsor", "official wireless carrier", etc. (I have no idea if SLU has such.) Sometimes sponsors locked out of exclusive deals use player sponsorships to "break" the exclusivity, especially when there isn't a labor union governing this kind of thing, definitely the situation here. Imagine for a second, if Verizon tried to sponsor a player to undermine TMobile. (again, have no idea whether TMobile's SLU sponsorship is exclusive.) In that situation of using a player-only sponsorship to defeat another sponsor's SLU exclusivity, it would be a definite no-no on use of marks. But what about a player sponsorship in which there is no exclusivity involved, but it does compete with an existing sponsor. An example might be selling players to an automotive dealership group that competes with Bommarito Automotive. (again, I have no idea if that is an exclusive deal.) But what would Bommarito say if 4 or 5 players signed a deal to make personal appearances at a competitive dealership at half the cost of a SLU sponsorship? SLU gets nothing. Players might undermine an existing sponsorship. My opinion: no marks. And I don't really like the thought of it. 2) Small, mom & pop sponsors for personal appearances. A pizza parlor, for example. It's kind of a tough call. They're not likely ever going to be a SLU sponsor -- too small. So probably no loss of revenue that would have come to SLU. And it helps in building local goodwill. But in allowing use of marks, SLU might lose control of how its marks are used and which brands they're associated with. The player would control. Not good. Trying to police this for all their players? A nightmare. On other hand, SLU doesn't want to anger its players. Tough call. Maybe no SLU marks. But simple "SLU player" in ad copy/text is OK. A mess.
Perhaps a solution would be a joint Athletic Dept/Players sponsorship sales strategy with rules governing. It would offer a stronger array of options, opportunities for both $$ (short and longer term) and co-marketing. But there may also be legal/anti-trust limitations for SLU, too. While SLU certainly owns and controls its marks, in the interest of protecting its sponsors and sponsorship pricing, can SLU actually limit the sponsors its players sell and the prices they charge? I'm not sure. The players don't have a labor union to negotiate these kind of things.
Sorry if I've gotten too far into the weeds on this! But it's a complicated subject, actually way more so than I've highlighted. There will have to be much discussion, processes, rules, approvals, etc put in place. And lawyers. Getting a headache just thinking about it! (no offense to the many great lawyers on this board!)