Don't take my word for it, but from what I've heard from others on this board, yes, this should be all right. If both teams are registered ASA and the umpires are registered ASA as well, everyone's covered by Bollinger's Insurance.
However, it would probably be best to talk with your local ASA commissioner for verification. You may look his contact information up here:
Amateur Softball Association of America (ASA)
Also, it'd be best to verify this with Bollinger's, as I am not a Bollinger's representative. Their website is here:
Softball Insurance - BollingerASA.com