Does your girlfriend often mention her mom's her best friend? Is she close with her dad? Does she frequently head home for sit-down dinners with the fam? Then yes, you should definitely ask their permission. It’ll mean a lot to her—not to mention them—in the long run, and unless you’ve done something to really piss them off, it’s doubtful they’ll say no.
If she hasn’t talked to her folks in years, use your best judgement; but there's probably someone in her life to whom she constantly goes for advice. It's best to tell those close to her beforehand (just mention it—you don't have to give dates if you think they'll spill the beans). It's a respect thing—not to mention they might have answers to any questions you have.