Yes. The governor would also call a special election to fill out the term and the appointee serves till then.
If the legislature does not object, the Governor can forgo the special election.
It would save the state a lot of money not to have a special election, but to wait and have a race at the normal time in 2018.
Would the special election be held before November 2018? I would hate to stake the Senate majority on another roll of the dice before then. I don't care how safe people think the seat will be. Personalities come into play, the candidate can have a brain fart and says something stupid (or something made to look and sound stupid after editing), voters would have a chance to react against Trump, skeletons come out of closets, the Democrats might find a superstar, etc. Too many things can go wrong. If it were up to me, I would NOT risk the seat.