Fieldmouse,

Any safety strap is better than none, but the chest harness can be very dangerous if you fall. Many hunters get into big trouble after they fall and are hanging from the tree. A chest harness only, will restrict your breathing and you will pass out very quickly. If someone does not cut you down fast you will DIE!
Go spend $60 on a "Seat -o-the Pants" harness and learn how to use it. It fits over all your clothing and in case of a fall, will save your life.
Also, you should always have your strap set so if you do fall, you have a good chance of climbing back into your stand.
That said, I too check to make sure the strap is not in the way of the draw.

Gravity will always win, you can only hope for a tie!

Good luck, be safe, you are special to somone or many. Do it for their sake.

Happy holidays!