No, he could not. It is not within the power of the President or President Pro Tem to decide whether or not a session is convened. Before recessing or adjourning, except sine die, there is a time fixed for the next meeting of the Senate. Whomever may be presiding has no authority whatsoever to ignore, delay, or otherwise fail to act in accordance with that order.
For all this conspiracy theorizing about how the Vice President could thwart the Senate from coming back into session, keep in mind it would be unconstitutional to do just that. Neither house can be out of session for more than 3 days without the permission of the other house. See Article I, Section 5.