They'll definitely re-use that set. 100%. Just - if the Pike-show doesn't come together - be prepared it's going to be the bridge of a 29th century Pakled-vessel in the 3rd season or something.
But stuff like that doesn't go to waste. Neither did the Shenzhou bridge (served nicely as the S31-vessel), or the Klingon Sarcophagus ship (which has been cannibalized and pieces appearing in literally every alien set). You'll get to see this bridge, or at least the individual elements, a whole lot more. They might just wear a new set of paint.
It'd still be a shame if we didn't see the Enterprise again. I really, really want to see the engine room.