As shown in the pic, my one-piece tub/shower was installed poorly. There is a gap between the vinyl top layer and the tile floor. To make it look better I was thinking about caulking it, but I think the gap is too large (up to about 1/4") and there's nothing but air behind it. Recommendations would be appreciated.
You certainly can, if you do it carefully. Here are my tips:
Use clear silicone. Any color (including white) will be much more conspicuous over the grout joints. Clear will transfer the existing colors and blend much better, almost disappearing.
Run a roll of masking tape along the floor, tight to the tub. Once you've tooled your caulk you can remove this for a clean line.
Cut the tip of the tube small. You want it to fit the smaller areas of the gap well to minimize squeeze-out. At the wider areas, slow your slide rate to allow the gap to be filled well.
Inject a substantial amount of caulk into the gap. You don't want a wall of caulk that will collapse. You want a solid rope.
Be sure the gap is completely dry when you apply the caulk. Silicone doesn't grab wet surfaces.
Tool the caulk with a finger, wiping the finger clean on a rag often. You don't want excess caulk oozing out around the sides.