I alternate between introvert and extrovert. I think the answer is yes: when I'm in an extroverted mood I tend to casually flirt with other girls and that does make me think less about a girl I'm really in love with, at least for a short while, it works even if I know the girl I'm flirting with only wants attention. It also increases your confidence so when your in a "wait, was that a signal from her, does she actually like me?" situation you're more likely to think "yes, that other girl flirted with me, so why not her too?" instead of the usual "nah, must've been my imagination, she couldn't possibly be into me..." self-defeating thought that introverts tend to suffer from.
Its possible for introvert and extrovert guys to become really obsessed with crushes. The difference being that if the person has a more active life style, they will have more to occupy their mind. From my experience, the introverts are the type that will not initiate conversations with you but they'll stare a lot, follow you around and want to be near you. It does come across as kind of creepy. I've had a few guys do this with me, one of which had a girlfriend.