Andy:

I've done more than my fair share of wall tiling around tubs, and you'd probably be better off taking that drywall down and using a proper tile backer board like Hardibacker, Wonderboard or Denshield instead.

The reason I'd be reluctant to caulk the gap between your tile backer and the tub is that you have a fiberglass tub, which isn't nearly as durable as an enameled steel tub. So, in future, if you ever have to redo the tiling around your tub, you'll have the problem of removing any caulk you put in there, and that's likely gonna be hard to do without damaging the finish on the tub. You don't really need to caulk that gap either. If your bottom row of tiles hangs down in front of that gap, and you caulk the joint between the tiles and the tub, water's not gonna get into that gap.

But, if it were me, and I was dead set on filling the gap between the tub and tile backer, I'd put masking tape all over the tub and bottom of the tile backer and then fill that gap with expanding foam. Once that foam is cured, you can cut it off flush with the tile backer using a razor knife.

Personally, I think it's better not even to fill that gap. I've tiled all 21 bathrooms in my apartment block and none of them had that gap filled with anything. Most of them were done 15 to 20 years ago, and so if there was a problem associated with not filling that gap, I woulda seen that problem by now. So far there hasn't been any problem at all doing it that way.

Is this your first wall tiling job?