Not necessarily would, but yes, he could, if an hour of the day always changes when he jumps through time, and he expects it to be different again. He would have to have a companion to make this question sound naturally, though. A passerby from another era would give him a strange look.
That's the primary distinction of "теперь" - implying that something changes.
Unfortunately, "сейчас" is often used in the same sense and things are muddled up.
One meaning of "сейчас" for which "теперь" can never be used:
(Lingvo)4) (очень скоро) (very) soon
он сейчас придёт — he'll come here presently / soon
я сейчас вернусь — I'll be right back
(я) сейчас! (иду) — (I'm) coming!