If you are painting something large, like a truck, would overspray on the trail side of the air cause problems?
Potentially, yes. A lot of large equipment businesses have switched to downdraft booths for that reason, as long as the product does not require the bottom to be painted.
If you are having problems with overspray trailing off and ending up at the backside of what you are painting, contact your paint company. Sometimes they will adjust hardeners and reducers to make the paint more wet, so it actually melts in when it hits the back panels. When you reach that section with your spray gun, it will flow the paint directly over the top of that.
You should also be conscious of where you are spraying. With a crossdraft or semi-downdraft airflow, start at the front of the paint booth and work your way toward the back. If you work the opposite way, as you get to the front of the spray booth, overspray will drift over the top of the paint you just applied. If any dust or dirt enters the spray environment, it will also get caught in the paint.