Yes, this is a comon way to request another can of beer in a very small amount of words while still sounding coherent and sober. However, to me this sounds like somthing that a cave man would say to a bar tender after thawing out from a rest of several thousand years. I just try not to think of beer as a verb to get the full effect.
Bar Keep: What can I get you?
Cave man: BEER ME!