Oh if it is the clumping kind she can become impacted. She may have a blockage. It can occur with the non clumping too but not nearly as often as the clumping kind.

Keep a very very close eye on her eating & pooping and her overall personality. If she continues to act lethargic, has trouble with bowel movements, starts to vomit etc... get her looked at ASAP.
I don't want to scare you but this is something that can be deadly without operation.

In the future is it possible to gate off the litter boxes?

I personally never ever use the clumping kind for many many reason, this is one of them and the most important reason why.

Wishing you the best of luck.