I agree that it's great to be honest. However...I'd just suggest preparing your son that he might have some uncomfortable conversations as a result. Let me explain.
School #1 made their offer.
School #2 called 2020 a day or so later and asked about other offers, 2020 was honest. School #2 offers. We knew it was coming, but finding out about offer #1 got them moving a bit faster.
School #3 had been unsure about son for months. He told them about offer #1 and #2 and that he would be taking one of them (had a deadline). School 3 wanted "one more chance" to see him.
2020 calls School 1 and asks if he can move up his visit (was scheduled a couple weeks away). School 1 wants to know why, 2020 was honest and said he was on deadline from School 2. School 1 got very snippy on the phone and it was a very uncomfortable conversation for my son (basically bullied him and ridiculed him when he asked questions about School 1's program). Son decides he doesn't want to play for a coach like that, and declines the offer the next day. School 1 apologizes for bad behavior on phone the previous day and said he was just "frustrated because things weren't going as he'd hoped." School 1 was out of money for 2020 kids and just couldn't make a competitive offer.
So it's down to 2 and 3. School 2 calls the night before School 3 is supposed to come watch him "for the last time." Turns on the sales pressure a bit. It is NOT EASY for a teenager to handle those kinds of conversations. The coaches are grown men with much more skill in "negotiating" and "sales" than a young teenager who is taught to submit to authority.
We ultimately chose School 2, which was the absolute best choice, but that last week when all the calls were happening were VERY STRESSFUL for my son. Once you start sharing info (and I agree that you should), just please prepare him for the phone calls and other pressure that will come. We weren't ready for it.