The Senate can make that 30 hours be an instant, by unanimous consent, and has done so on occasion. See numerous unanimous consent agreements calling for a cloture vote, then "if cloture passes, to move immediately to vote on ..." It is typical, however, to treat the 30 hours as a literal 30 hour clock that runs whether the Senate is open for business or not. I've never heard an objection to the protocol of counting the time that the Senate is shut down for the night against the 30 hours of post-cloture time, nor any objection to the clock running while the Senate is open but idle (the routine "quorum call" condition). The relevant language in Rule XXII is:
After no more than thirty hours of consideration of the measure, motion, or other matter on which cloture has been invoked, the Senate shall proceed, without any further debate on any question, to vote on the final disposition thereof ...
Hussein’s gangsta from the moon -— lunatics