I just bought SWTOR and I never liked casual questing. Can I grind to 50 with PvP and then go back to the story missions at my leisure? Or will being too high of a level inhibit my ability to accept these missions?
While there's nothing stopping you from accepting (and completing) any quest below your level (as long as you haven't finished it previously), enemies will not scale to your level.
There is a hard-mode version of every flashpoint in the game that unlocks when you hit lvl50, though I'm not sure if you have to complete the regular, non-scaled, version first.
All your class story quests will remain available, and you'll even still get offered all the area quests of the places you pass through pursuing said quests. (I just had occasion to go back to Taris with a level 47 Republic char -- Taris is intended for level 16 republic -- and I got offered just about all the quests I hadn't done on my first pass through plus the daily heroics).
However, all of them will be scaled to the level Bioware estimated you'd be at playing just the regular content in the regular order, so get ready to sleepwalk through a whole lot of completely outleveled content with bosses that are tedious bags of too much hit points rather than actual challenging threats... But the story's pretty good.
Yes you can, but if you 'grind' to 50, why go back to the class quests if you were not interested in them in the first place? May I suggest a (hopefully more fun) approach? Only do your class quests (i.e. don't accept any quest givers), and do PvP to supply the rest of the exp. So, if the class quest has a suggested level of 17 and you're 15, do PvP to 17 and do your class quest. It's not only more varied (you don't burn yourself of either pvp or pve) but you also get to do the very fun class quest fights at the level they are supposed to be done (so you get to do fun and challenging battles you can actually lose). Just a suggestion.