In terms of water ingress into the stud space, the tub surround will be 1/4in high on the sides of the tub, but the lip of the tub stands high enough to lip behind the surround. You can check this by measuring the height of the tub's lip and comparing to the "droop" of the tub.
However, you might have water standing at the lip if the current slope prevents it from flowing into the tub. Assuming this tub is also used for showering, you'll have build-up of soap residues as water accumulates and evaporates while standing in the corner.
To caulk the seam you could aim for the tight gap behind the surround where it touches the tub lip, rather than try to fill the entire 1/4in gap. First do a dry install of the surround, then for a final install first apply caulking to the tub's lip, rather than applying it after the install. Ensuring you have the upper 1/2in or so of the lip caulked.
Alternatively, you could try lifting the sides of tub by installing a piece of 1x or 2x support lumber. The length of it should be about the width of the tub. Carefully jack the tub ends up with some vertical lumber, fastening the support lumber to the studs. Let the tub's rim bend a bit but do not lift the tub off its base. This could compensate a good portion of the 1/4in drop, but possibly not all of it.
Be careful not to put too much upward pressure on the tub rim so as to lift the tub and make theses supports the hanging points of the tub; you still want the cemented bottom to be the base and carry the bathers'/bather's weight.
You could then add a bit more cement to the base of the tub around the head and foot end, to provide support for the minimal lift that may have occurred here. Simply slap the cement against the tub's underside & floor.
