According to the rules they are supposed to unless they have a team in an IASF division, which would be allowed to compete at the Summit, as well. Per the website:
Varsity Spirit - The D2 Summit
Can a Division II program receive a bid to The Summit taking place on May 2 – 5th?
Yes, each PROGRAM must declare which bid the WHOLE PROGRAM will be competing for at each event. A PROGRAM cannot compete for a Summit Bid and a D2 Summit Bid at the same event. You MUST declare before that event to which bid your PROGRAM will be competing for. Once a team in a program wins a Summit or D2 Summit Bid, the WHOLE PROGRAM must stay on that Summit Path for the remainder of the season.
Can a Division II team compete at The Summit in the International Division and also compete at the D2 Summit?
Yes, teams can compete in the IASF divisions at The Summit, BUT those athlete will only be allowed to compete on ONE team at the D2 Summit. Please see the crossover rules for additional clarification.