We have just installed the cement board in our tube enclosure, and my husband is thinking about sealing all the joints with silicone caulking BEFORE applying the tile adhesive, tiles and grout. (This has nothing to do with the application of silicone caulking AFTER the tiles are up and the grout has cured a few days.) So, will the adhesive and grout be able to adhere well to the corners and seams where he plans to apply the silicone caulking first, or not?

Probably not well but if the joint is very small you may get away with it. I'd use a urethane caulk instead but usually, caulking is not needed as the tile mastic will seal the joints. Silicone caulk afterwards.

So, will the adhesive and grout be able to adhere well to the corners and seams where he plans to apply the silicone caulking first, or not?

Seeing as how the original post was Saturday and you've had a full weekend day and half of today, this might be too late, but here goes...

No, the thinset will not stay bonded to the silicone in the inside corners of the cement board or the cement board joints within the wall field and having that little bit of area where nothing bonds is a completely 100% non-issue as well, you'd never even know about it. I do think, however, there is a misunderstanding on the purpose of using thinset and alkali resistant tape on the joints. In the inside corners, not taping those joints and using silicone really won't be all that big of a deal, since it's a movement joint, whatever thinset is used there to tape the joints is going to crack anyway. A bigger concern is the joints within the walls where two sheets of cement board join. Cement board joints are filled with thinset and taped so that the boards act as one large monolithic sheet of cement board. Without the tape and thinset, the pieces are more prone to moving independent of each other resulting in cracks in the tile.

Filling the joints with silicone prevents the proper sandwiching of the backer tape and it won't create as strong of a joint. Making that small spot between the two sheets of cement board waterproof with silicone is ridiculous when the entire rest of the sheet provides no waterproofing at all. Waterproofing a tub or shower surround requires the use of a moisture barrier attached to the studs and overlapping the flange of the tub or shower pan (or liner for site built mud pans) with most commonly 4-6 mil plastic sheeting or 15 lb roofing felt aka tar paper-OR-using a surface applied waterproofing membrane on the cement board itself, such as Redgard at HD, Floor & Wall watertight from Lowe's, Kerdi, Nobleseal TS, etc, that provide waterproofing just behind the tile and in front of the cement board.

Furthermore, in terms of adhesive, the best setting material to use in a wet area, and the only one you should be using is thinset, from a bag, mixed by you. Anything that comes ready to use in a bucket should be left for walls in dry locations only.

Good luck