Well I do during both xbow & rifle season in WI if it gets cold and I need a bigger coat to stay warm. I'd much rather have my harness fitting snugly with proper fit around my body and I see no problem doing so. With the Safety Harness on and my big Ole Blaze Orange coat over it I still have ease of movement. And I am warm.
I do take the Tree Tether strap and tuck that in my chest pocket of my outer coat. And I also wear a shoulder holster too.
Fact is even before I have left camp my Safety vest is on. Now the Safety vest is over my Bib overhauls with the leg straps but is under my outer coat.

But read the Safety Literature that came with your vest. Prepare your outer clothing as below. With those extra leg relief straps.

I do have an extra Tension Relief strap/foot sling in my Outer Coat Pocket if I should fall. I am not about to dig thru layers of clothing trying to find that darn thing. I also have one in a designated pocket of the vest. That vest pocket is all it is used for nothing more.
So do get another one. Make it easily accessible if for some dumb reason you fall.

Another thing I went to is those Carabineer Safety Clips. It helps weight my Safety vest strap which makes it easily found and does help keep the tether end in my chest vest pocket. So the Tree Tether Strap of my vest comes up the back inside the coat and over my left shoulder to the front of my chest pocket.
I also have a Carabineer on my Tree Trunk Strap. That I leave to the tree when I quit for the day. That way I have no fooling around in the dark coming and going. I have added a tubular foam piece of pipe insulation around the connection once they are together. Helps keep them quiet. The Foam is slit, you just slip it over and is tethered to the tree strap with a piece of twine to the strap. Quick and simple.

In addition I use a Prussic Knot Tree to Ground tether.......I am tethered from the time I leave the ground to the stand and back. Overkill? Maybe. But then I am an old fat guy who sits a ladder stand.
Can't fall out of a ladder stand? Wanna bet?

Besides I teach Hunter Safety ~ If you can't talk the walk - them don't walk the talk....I hunt like I teach and teach like I hunt.

Hey have fun but be safe out there!

JW