You absolutely can, depending on where you want to live.
If you want to be able to bike to downtown, you'd probably have to buy in an up-and-coming neighborhood (meaning kind of sketchy now, but will likely be gentrified in another 10 years). Outside of downtown Raleigh, bike commuting is less feasible, but by no means impossible.
If you want to post links to some of the houses you saw, I can tell you what the neighborhood is like there.