The NCAA does not allow softball players to play on any team during the summer. There are no leagues for them. They can't even play on city or church league teams. They can play on US teams like the US National Team if they can make the roster. I don't know about signees, but I would guess that they couldn't play if they were enrolled in summer school.
Someone suggested that this was the tradeoff for allowing them to play games in the fall semester. I don't know if that is true. It seems to me that legally something could be done since men do have summer college leagues.
This information was given to me by a NCAA Division 2 player, but I believe it applies to Division 1 as well.