red wrote:
The patient is a shower stall, acrylic base, cement backer board, 8x10
tiles in thinset. The tiles overlap the lip of the acrylic base by
1/2"(?) and there is a 1/4" gap between the bottom row of tiles and
the flat top of the base. I went to start grouting, and noticed that
the gap behind the bottom of the tiles isn't always filled with
thinset.

Is it necessary/desirable to try to push thinset/grout under the
bottom tiles and into the gap behind? Should I just squeeze extra
caulk up into the gap? Caulk seems easier, but won't support the
bottom bit of the tile as well.

Any advice appreciated.

Red

The joint between the tile and the base should be caulked, right? One
assumes that the space not covered by thinset should be very small, so I
would not worry about it - it would take a freak accident to break it.
Normal caulking will probably fill it, and I would be inclined to do the
caulking in two stages to allow those gaps to cure comepletely before
doing the final line.