Olympus OMD EM-5 body + the 45mm as my only lens (is it possible?)

I've had the 45 1.8 since I got the EM5 last April, and it is definitely a keeper.

You might look for a used general purpose zoom, like the Oly 14-42 or Panny 14-45. When they turn up, they don't usually sell for a lot, in the $100-150 range. It sure is handy to have a general purpose zoom, so you aren't repositioning yourself a lot for casual shots.