First, a properly built shower is waterproof without the tile on it, so no, neither the grout nor sealer will solve the problem. Drywall as a tiled surface in a wet area is never allowed, and does not conform to any approved methods. I think you're likely to need to tear out and re-do. Since they used drywall for the walls, they probably committed other errors in the whole construction as well.
There are numerous approved methods, and lots more ways to do it wrong. Any of the approved methods works, but some have some interesting attributes that can make a good shower better. Even if you don't try to do this yourself, you should read up on how a proper shower is supposed to be built. Most of those are documented in the TCNA (Tile Council of North America). You can buy that handbook, or verify that the guy doing it is familar with it and will sign off that he is using one of the approved methods. One good place to review some of the techniques is www.johnbridge.com 'Tile Your World' forum. My favorite method is Kerdi from www.schluter.com, but there are many other good methods out there. You can view their site and watch some of the videos they have. Personally, I'd use a surface membrane to waterproof the enclosure directly beneath the tile. Tile is decorative and a wear surface, NOT the waterproofing layer.