Perfect solution for just that; as example:
until recently I had a 2010 mac mini (dual core 2.4Ghz, 4Gb RAM, and 6 Tb Media drives ) driving entertainment to: 6 x Apple TVs, 3 x iPads, 4 x iPhones, and 5 x Macs. On a typical evening, 5 TVs would be connected and streaming Movies / TVs shows.
The Mac Mini also had Plex installed to provide more US network channels to the Apple TVs, using PlexConnect
https://github.com/iBaa/Plexconnect.
The 2010 mini's basic spec by today's standard was more than enough for this.
The only reason I replaced it for a new one was to upgrade to Thunderbolt, and to also have some extra processor capacity as an additional backup OS X Server (local DNS, DHCP, Mail, Web, MySQL, Xcode bot server, Git code hosting, Backups, ...)
As I said they're more than capable.