Before I owned one I would have said no. But after trying and then purchasing one I will never go back to onboard unless there is a drastic improvement. I would sooner give up a multi gpu setup than part with my ht omega (which I did).
But getting a cheapo card won't be noticeable as has already been said. And your output system will need to be of quality as well. I just had the opportunity to try a pair of audio technica ath-1000x and I will be picking up a pair as soon as I find a reasonable deal. They sounded wonderful.
But remember audio is in the ear of the beholder. What sounds good for one may not for another.
If you can, try to get a chance to listen to different setups to see what you like. I listen to a lot of movie scores (OSTs), trance, classical, rock and metal which I find my setup to excel at. I do want it to be a little tighter with some more bass and mids and the ath-1000x sounded incredible, a vast leap from my atha700s. Not to say that they are bad phones, they've been amazing for the time I've had them. Plus the first time I played BC2 with my setup was an absolute sensation for my ears.
My 2 cents.