you might consider using backer rods to fill the area before caulking, but I am skeptical of the rods in that critical of a spot.
I would use your plan, back fill with good high quality silicon caulk to go behind the scenes. Let dry for a good day and a half depending on ambient temp. Then fill in the front and make that bead into a ramp if you will with your finger dipped repeatedly in alcohol. This will shed the water from the walls to the tub sides and down in the tub itself. This will work and will also flex when the sides come into stress.