Assistant professor position in the USA. Can any leftover startup money for equipment be used to pay students or my summer salary?
This varies not only from university to university but from department to department. In some places it wouldn't be a problem, and in others it may even be impossible.

I recommend you get in touch with whoever your point of contact is (whoever extended you the offer) and ask them directly. It is important that they know you want to do this as this will naturally affect how much startup funds you are liable to need.