Yeah, they will hide. Plus he is new, which is more reason to hide. Many gobies, jawfish, dartfish, tilefish, and wrasses can often disappear for days or weeks.
If you’re concerned, check your overflow, check the floor around the tank, check your sump... if he is nowhere else, then you know he is in your tank.
Now is he alive? Thats more complicated to answer. Assuming he wasn’t sick or with a parasite, and assuming your livestock won’t kill/eat him, you can ask yourself how long has it been. The longest I’ve seen a fish go without eating and still survive is 6 weeks, but 3-4 weeks is normal.