If you buy person-to-person, yes, in most states. However, just because a felon (or a marijuana user, both are prohibited from owning guns) can buy a gun like that, doesn't mean they won't get in trouble for it if they ever get caught.

Edit: form 4473 question 11e asks if you are an unlawful user of drugs such as marijuana and reminds you that it is still federally illegal. You will fill out this form if you purchase a gun from a licensed dealer. Lying on this form is itself a felony.