A safety harness is designed to prevent you from falling to the ground. When you attach it to the tree, you should have the strap taught when you sit down. That way, if you do fall from the stand, you won't "fall" far and you should be able to get back on the stand. Too much slack in the strap, and you might not be able to pull yourself back on. Hang long enough and it will pinch off blood flow.
Harnesses are much better than the old "belts" that first came out. During certification for Hunters Ed instructor, we were shown a video put together by a instructor group on how to wear the "belt" properly. The video showed a guy (a big, strong guy) wearing the belt around his waist. He rolled off the stand and the belt rode right up to his rib cage. As he was trying to get back onto the stand, you could tell he was struggling and was having problems breathing and then you could see the panic set in (even though this was all staged). If it hadn't been a demo, and the other 3 guys weren't standing there, he wouldn't have made it! He couldn't get back onto the stand and couldn't breathe. Point being, with the belt, wear it up under your armpits. Wearing it there, your weight is under your arms and not across your diaphram.
Given the harnesses they have on the market today, this senario isn't a problem. Your weight is more evenly distributed. There is still a possibility of problems though. Read the instructions that come with the harness and heed them. There are instructions for a reason.
One other thing I learned and do is to place a tree step just below the stand platform. In case I would fall, I would have something to step on to help take weight off the harness and help assist me back up.
Safety is #1. You can never be too careful.