My .02
If you can find a real strat that you like, and you've actually heard it give you the sound you're looking for, and you can afford it, then buy it. If not, try the Squires. See if you can find one that you like the way it plays. If so, buy it and 'pimp it'. Most guys that buy real strats spend all of their time pimping them, too. No one's ever satisfied with their pickups. Will a cheapo undure heavy-handed mods like swapping out the bridge/tailpiece for a totally different kind? No, but if all you need to do is upgrade the electronics and tuners on an axe that you are happy with otherwise, go for it. If you're looking to build the ultimate machine that you'll be happy with the rest of your life (let me know how that works out for ya), then yes, start with a higher quality base.
Admittedly, a lot will also depend on how much you play. No more than I play, a Squire does me just fine. If you keep one in your hand every waking moment, then maybe you need something better.
However I did see Victor Wooten and his brothers a couple years back, and his eldest brother, whose playing is so incredible that I can't even describe, played a Squire, not because he was paid to, or even because it was free. He just liked it better, and he said it was one the few guitars that had ever been able to hold up to his treatment of it. He had been playing it for a few years at that point, and it seemed indestructible. Maybe he just got a good one.