That sounds reasonable if organics are floating around freely in space. If they're restricted to comets and comet fragments, then dispersal without an atmosphere would be difficult.
I've always felt that comets were rather odd, BTW. I mean, they're described as being huge conglomerations of water ice and miscellaneous space detritus. They're as much a fixture of our solar system as planets. How could such things have been created in such numbers?
What part of the moon does not have a crater on it?
Next time some wiseacre kid of 4 asks why the sky is blue or the grass is green, fire that one back at him. Maybe he'll take up science as a career and figure it out and tell the rest of us.