There are a few exceptions, but for the most part, most of these guys (on the Celtics SL roster) are competing for a 2-way slot or trying to showcase to other teams. Walsh is one exception. He was offered and accepted a contract. He is booked and will be on the roster for for at least 2 years, unless traded or waived. Banton, may play in the SL but in any case, he is also guaranteed for 2 seasons. These guys are no longer "trying out". They are signed. Champagnie is signed but non-guaranteed. In many ways, he is no different than the FAs just trying to showcase.
Davison is a little different. He has a 2-way QO from the Celtics but I think if another team offers him a regular contract, we can match. I don't expect any other team will offer him a full contract so most likely, he ends up on a 2-way for another season. But if he plays well enough, who knows, he is officially a FA, he has not signed a contract. So he is very much in "try out" mode, or should be.
I think from the Celtics point of view, there is not anyone in the summer league, our roster or otherwise, that we are going to sign to a regular contract. Maybe some camp contracts (I forget the official name for these) but most likely, the Celtics will be taking on 1 or 2 more players for 2-way contracts. I think they can offer these to any eligible players on any SL roster (or players not on SL rosters), but it seems as though they are going to get the best look at the players on their SL roster.
It is fun to watch these players, especially the ones who have not been on the Celtics, but all the ones that likely matter, have already had their contracts resolved, or in the case of Davison, is pending. All that is left is to see if there is 1 or 2 2-way player to pick up.