I am not a lawyer, so fiddletown will no doubt come by soon and correct me. But ... I have read a bit about this.
First off, there are two levels of restoration of rights: state, and Federal. The Federal restoration process is on the books but our Congress has explicitly denied funding for the process for many years, so it might as well not exist. So, someone who is a felon due to a conviction in Federal court is out of luck unless he/she can score a presidential pardon.
On the state level, it gets murkier. We have 50 states, so there are 50 different sets of laws that apply to restoration of rights. Technically, if a felon convicted in a state court has his/her rights restored according to that state's process -- that should be the end of it and he/she should be good to go. However, although I don't recall specifics, there have been cases in which the good ole BATFE has unilaterally decided that they didn't agree with a state's procedure for restoring rights, so they declined to recognize the person's rights as having been restored and
persecuted prosecuted him as a felon in possession of firearms, notwithstanding the state restoration of rights. IIRC (which I probably don't), it had something to do with "expungement" -- like maybe whether or not expunging the record of a conviction is or isn't the equivalent of restoring the felon's rights.
Bottom line -- it does not apply only to purchases through an FFL. A convicted felon who has not had his/her rights restored cannot own, "possess," or even touch a firearm. They can be arrested and charged if they even live in a house with someone who is not a prohibited person and the gun(s) are not locked up to prevent the felon from potentially being able to access it/them.
If your question is asked because of a specific person and case -- I would advise you to advise the person to ask a good attorney.