I can't imagine that there would be a problem as long as you're not flashing into the players' eyes. The XL Center in Hartford is alive with flashes all through UConn women's games.
They don't look too bad to me. Maybe a tad underexposed but that's about it (I'm sure there's some noise in there as well but it was very noticeable at that small size). I know D1 lets use strobe, but I guess that's not that helpful for you. I would just ask the school.
Thanks everyone. I work for the school so permission on that end should be pretty straight forward. If Div I allows strobes I'm sure Div III does as well.. Thanks for helping!