So me and my friend who are starting a band have a chance to play at an open mic night for start up bands. Sounds like a great chance to get out there and play some music, but right now its only me and him and we only have an electric and acoustic guitar. We want to add drums and bass, but haven't found anyone yet.

Should we still go out and play with just us? Or should we wait till we have a full band? The gig isn't anything serious but I don't want to look ridiculous if we don't have a full band. Also we are a mix of folk rock/70's hard rock if that helps at all
I think you can pull off folk rock with just the two of you. Just make sure the electric is mellow (maybe play clean slide). Do simple stuff, and pull together some real simple harmony vocals. Good luck. Sounds fun.

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It can work in this instance because you guys are just a duo. Hopefully one or both of you is a singer.
And no, Guitar Hero will not help. Even on expert. Really.
There are lots of bass/drums backing tracks out there if you plan on doing covers. I've done this at open mic before when I was "between bands". It's kinda nice, 'cause you don't have to worry about your rhythm section F'ing up your act.

Try www.guitarbackingtrack.com

Lots of stuff there for practice and play, many with vocals.

I've also played with a drum loop into the PA at open mic. Give it a try, and see how it sounds. You might be surprised.
At the bar I used to work at we had a two man band come in a few times a year. Musically they were fine but at a place like that it lacked the energy of a full band. Two people and a drum track should be good for an open mic though.
It's an open mic. It would be fine to play it by yourself. The whole point of open mics are to go out and have a good time and let people here you. There's no point in waiting to find musicians. Start playing it as you are now and as you acquire more members have them play with you. It's not like this is supposed to be a proffesional act you are presenting