I am also applying this cycle, so I have no real insider information on this, but I wanted to share my thoughts and also ask others.
From what I have read and heard, the "thing to do" is to wait until you get waitlisted to send a letter of intent. I guess the idea being that A. You have had time to think about which school is best for you. B. It is unlikely that a letter of intent will sway them from rejecting you over to accepting you.
While I can understand both of those reasons to wait (someone correct me if they aren't the reasons plwase), I actually see it kind of differently. If you have multiple acceptances already, and you have taken sufficient time since your interviews to think about which school is the best fit, and you have real reasons why you think so, I don't see why it isn't actually STRONGER to send one before getting waitlisted (other than maybe doing it when you didn't have to--if you were going to get accepted anyway). My reason is that if you are sending it before you have a decision from them, they may be less likely to think you are only sending it in because you are desperate and need an acceptance at the end of the cycle. This is all assuming you have taken sufficient time to really think about what makes this school the best fit.
I'm not speaking specifically about GU with this by the way, just general thoughts.