Can you install Minecraft mods on Ubuntu?

You can but I don't know how to do it.

What sort of mods (client or server)? I have run plain vanilla minecraft client and server and Tekkit modpack client and server in Ubuntu. Basically minecraft is all java, although, and I have never had any trouble with any mods using openjdk7-jre (I have not used Oracle Java in Linux since Ubuntu stopped supporting that some years ago, which may have been before I got into minecraft while still beta).

So you may want to look around http://www.technicpack.net/ and see if you like one of the mod packs they have ready to go, either with their technic launcher for client and/or servers with compatible mods.