There was some thought that Parliament might force abdication in favor of Henry, who was young enough to, as theyw ould say, "have any Catholic influence negated." So, I suspect they'd try to force him to do this.
Charles I, in fact, warns Henry not to allow this when he speaks to them before being beheaded, according to Wikipedia. Of coruse, that's the equivalent of saying, "Some guy in a sports bar told me..." at times

, but it does seem like something at least a few considered who wanted to keep the monarchy. (After all, they also offered Cromwell the throne.)
My guess is he grudgingly does so for his own safety and that of his siblings, but has a secret agreement that Henry will then abidcate in favor of him again whent hey are restored. I would think you could do that and still keep your own spot int he line of succession. (In Henry's case that is; I dobut Parliament would let Charles II do that, so Henry would hve to sort of decree it upon their return.)