I've got a question. What kind of trem is it? Vintage style or is it a 2-point? (post a pic if you can)
Secondly, I'm not sure I understand your question. You can't raise the height on a trem and have low action at the same time, that makes no sense (unless I read your question wrong or unless you meant something else and forgot to state it). The intonation might go out of whack a little but it shouldn't be an issue to fix on a Strat. All you need is a phillips screwdriver and adjust it clock or counter-clock wise, it's pretty easy.
With any
Strat trem, you can, however, raise and lower the height of the saddles to get them adjusted to the proper radius of the fretboard. Keep in mind that if you start adjusting those (raising or lowering them), your strings will either buzz (if the saddles are lowered) or be too high (if the saddles are raised).
Fender recommends a 1/8" gap between the tail of the trem and the body's surface. If the saddles have been adjusted and are not at the correct height, you can order a tool from stew-mac that will let you adjust them to their proper height, according to the radius of the fretboard.
Jimmy
