The obvious answer is yes, you can! The question is if you really want it, because it will be easier to achieve an appropriate metal sound with humbucking pick-ups. Today's amps or (modeling) effects provide you with insane amounts of gain, so gain is no problem, even with (lower output) single coil pickups. As explained in topo morto's answer, hum can be a problem, but using a noise gate, not standing too close to the amp or to other sources of interference should be sufficient in most cases. Remember that many rock guitar players use(d) single coil strats at high volumes and relatively high gain settings (Jimi Hendrix, Ritchie Blackmore, Yngwie Malmsteen, etc.).
One useful option is to change the wiring of your single coil strat to allow a series connection of two pickups. Note that this is different from the parallel connection achieved by two positions of the 5-way pickup selector switch. A real hum-bucker uses a series connection of two coils. I've added that option to my strat and it achieves a hum-bucking (i.e., noise canceling) effect, and a sound that is darker and fuller than the original single coil sound. It does sound different from a "real" humbucker though, and honestly, I don't use it that much because even for high gain sounds I found I like the original strat sounds best (I don't play metal though).
Note that this answer only refers to the single coil pickups in your original stat, not the strat as a guitar model itself, because it's probably obvious to you that you can replace the pickups if you like, even without replacing the pickguard.
In sum, you can play metal with a single coil strat, you can even play metal with a ukulele (
), but the question is if it's worth the additional effort to achieve the sound that you like.