Q:Can I play as my amiibo in Super Smash Bros. for Wii U?
A: In Super Smash Bros. for Wii U, players can battle against amiibo fighters, team up with them, or send them in against your friends' amiibo fighters in a multiplayer battle. Players do not have direct control over their amiibo fighters in-game.
Unfortunately, unlees I missed the information, the FAQ about Amiibo doesn't seem to expressly state whether these can be used online or not, but you could give a call to Nintendo's 1-800-255-3700 (6 am ~ 7 pm Pacific, everyday) Customer Service number, or use their webform to contact them, and one of the service representatives should know if it can be, or if there is some special way you have to set up the matches or not.
And perhaps you could come back here to let us all know what the answer is, as I'm sure there will be a lot of others wanting to find out as well.