By using the tools here, you are promoting FAA as much as yourself. There are plenty of email newsletter providers out there that won't be branded with anything other than your own work. It's just silly to be sending out newsletters with links to promote work or websites other than your own. The owners of this site are very clever, always with a hand in artists pockets. And don't tell me it's not intentional.
To answer your question, no, there is no benefit to show both other than to this site. You're only going to confuse your subscribers with which link to click, and if it's the FAA main link, you lose, FAA wins.