To me, there isn't one yes or no answer... I'd say it all depends on the situation.
I would not be involved with a man who I'm not physically attracted to. I've tried it and no matter how much I tried to turn my like into love, it didn't happen. And these weren't ugly men either... I just wasn't feeling them like that, and no, they never grew on me.
(I think what one poster mentioned about needing 3-5 dates to figure it out is true.)
Now, there could be a problem if your "type" is so constricting that you are attracting the wrong man. If a woman can only be attracted to bad boy types and ignore the nice man who is still assertive and confident, but just not thuggish, then yes, that's a problem.
If you can't find yourself attracted to anyone but the 6-foot-2, bald, dark chocolate brotha, then yes, there might be a problem.
Like another poster said, I really don't have a type. There are certain looks that I find more attractive than others, but I really haven't had a relationship with anyone who fits that look. If one looked at pictures of my past BFs, there would be no commonality. I've gone from a dark chocolate muscular African brotha to a man who looked like he just got off the boat from Sweden. I've dated super-tall (6'7") to 5'7" -- and I can say the 5'7" man was the best kisser of all of them.
I've been on dates with men who look like they could be in GQ Magazine and I just think, eh. Then I go on a date with a man who should be on the cover of Computer Geeks Monthly and I'm in love.
A lot of that has to do with personality, and you may never know if you can truly be attracted to someone if you outright reject them on looks alone... or if you reject someone because you're not used to their type of personality.
So... while I'd say you can become attracted to someone who's not your type, don't force yourself to let someone "grow" on you if you've given him a fair chance and you're just not interested.
And Kia... as you try to figure this whole thing out, I guess you just have to be honest with yourself about whether you're restricting yourself TOO MUCH because of type... but at the same time, don't beat yourself up if you meet a "nice" man and just aren't into him.
P.S. What I've said applies to men who you actually enjoy being around and might consider as a future mate. If meet a certain man and you know from jump that there's no way in h--- that you could ever like him like that, then definitely don't waste your time trying to give him a chance..