You could definitely do that, and it would be great training for a one-arm pullup.
If at all possible, start working out with dumbells, as it will force each arm to lift its own fair share. Some great exercises are one-armed push-presses, each side, overhead presses, each side, one-armed clean & jerks and snatches, one-armed overhead squats.
If you're stuck with bodyweight only, try to throw in some offset training...the one-armed lowering that Klaymen mentioned, uneven-grip pullups (one higher than the other), one-armed pushups (I know you said your bicep, but you're probably uneven in all aspects of strength on that side) and lateral pushups, where one hand will start on a raised platform (a basketball works great) and you pushup powerfully and jump to the side, ending up with your other hand on the basketball.
Hope this helps!