you can swap out your mobo and cpu yeah, going with an i7 and a new mobo will be on the pricey side, since you already have an fx, have you considered an fx 8320 or 8350? in there are not many games that would have that much of a difference and you'd be saving about 200.00 or so.
as far as swapping everything out, you might need new ram (there is no guarantee that your current ram is compatible with the intel mobo you'd get) and it would be a good idea to reinstall windows. Both problems would be avoidable if you go with a better FX processor.
Also, if all you are going to be doing is gaming then you wouldn't need more than a good i5, the i7's biggest advantage over the i5 is hyperthreading and there aren't many games (if any at all) that make good use of it.