Probably not, but it depends on the garage door. I used to be able to open my neighbor's garage door with the remote for my own garage door. There's also the opensesame attack (replay attack, search for it). You can perform such with a YTS-0 (Yard Stick One). I still ordered a Flipper Zero. Its cute as hell, probably has a neat community, and its more portable than my PortaPack + HackRF or Proxmark + Blueshark.

Samy Kamkar who did Opensesame on the Radica Girltech also did a DefCon presentation about attacking rolling code remotes as well: http://samy.pl/defcon2015/