According to multiple websites, yes, Tony Moeaki made the roster in 2015. He was brought in for depth purposes in October, and I vaguely remember seeing him on the field a few times.
The Falcons tight ends have been an unending tire fire since Tony Gonzalez retired, and 2015 was no different. This should come as no surprise considering Thomas Dimitroff has drafted only two tight ends during his eight drafts: Levine Toilolo and Keith Zinger. This is essentially a recipe for an unending tire fire.
How did Pro Football Focus rate all four guys that played snaps at tight end? Bad. All received negative grades. Mickey Shuler had the best bad grade, likely in part to his 21 offensive snaps. Moeaki managed 91 snaps, and as you are probably aware of, did not do much with those snaps.
Moeaki had an impressive rookie and junior season with the Kansas City Chiefs, after missing his sophomore season due to injury. The Buffalo Bills, Seattle Seahawks, and Atlanta Falcons all tried getting a similar impact from Moeaki. Sadly, he has had such limited production that it appears his career may be in jeopardy. He caught three balls across 11 games for the Atlanta Falcons, with zero starts.
I had some outside hope for Moeaki when he first signed with Atlanta, but there is clearly very little to talk about with his time in Atlanta. He could not hop ahead of Toilolo in the pecking order, which is a very, very bad sign.
Atlanta could replace Moeaki with any number of late round picks. Free agency is full of underachieving tight ends, such as Dwayne Allen, James Hanna, Zach Miller (CHI), Clay Harbor, Mercedes Lewis, Vernon Davis, and Ladarius Green. Green would be an interesting signing. He has been a backup in San Diego for his career, but would easily become Atlanta's most athletic tight end. However, his failure to earn a bigger role is concerning. The Falcons may have to swing high for the likes of Coby Fleener, or they may take a shot on the ageless Antonio Gates.
At the very least, it will not be difficult for Atlanta to replace Moeaki's three catches and occasional blocking.