Water – Does the type of sheet rock behind a glue up tub surround matter

I don't have experience with it, but there are fiberglass-covered drywall products available. If that is not available, I would recommend using 1/2" James Hardie Tile Backer Board. The smooth side is smooth enough to be painted. As far as taping, I would use a fiber glass mesh tape and a joint compound mix like Sheetrock 90, which hardens better than pre-mix joint compound.

But to really fix the problem permanently, I would pull cut away the bottom 18" of drywall all the way around the tub, replace it with Hardie Tile Backer Board, cover it with Schuter KERDI and finish with tile. Google or Bing to get more information about those products and how to use them.

Tip I picked up from Mike Holmes: don't run the tile backer board over the tub flange that goes up the studs. Stop the tile backer board above the flange, fill with thinset and cover with KERDI. Use KERDI-FIX to adhere an 1/8" fold of the KERDI to the tub deck.

This all assumes this is a tub only with no shower.

As long as you have secure anchoring of the 6" strip of drywall to the studs behind, and since the strip is along the ceiling, strength is not a major concern here. Additionally, the primary reason for using joint compound is not for strength but to create a smooth work surface for finishing.

In applications where the drywall will be completely covered, such as with a hard paneling, installation can be finished with no mud/joint compound at all.

In your case, since it's in the bathroom, along the ceiling, as long as the strip is out of the splash zone of the shower I wouldn't bother with mud.

Now if your shower is unusual and the ceiling is in the splash zone, then waterproofing will be necessary and you should use cement board not drywall - but it sounds like drywall or plaster was already used, so replacing it with more drywall isn't a problem in this case. (Or, if it is, you have much bigger issues already with the bathroom that are outside of the scope of this specific question.)