Will using a tight sling while in the sitting position affect the point of impact enough to make a difference compared to just supporting my elbows on the bench?
Rifle is a Chapuis in 9,3x74R.

I guess not everybody has the same idea as to what a double rifle is for. I don't view them as bolt rifles and don't treat them the same.

The slings on my doubles use detachable swivels - no QD swivels, then no sling. I carry them in a coat pocket or day pack. They're attached when I need both hands free to climb with, or to carry something else for a short distance, then they come back off. I've never hunted with or fired a double rifle with a sling attached, and can't imagine wanting to do so.

My hunch is that a tight sling probably will make some difference in regulation with a double, but I've never tried it.
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"Serious rifles have two barrels, everything else just burns gunpowder."

Well, seeing my Chapuis sling swivels were held in place with a screw with a super thin screw slot and they would only hold about a 5/8 in wide sling I removed them and just added QD's. Once I get this shooting minute of moose at 100 yards or less I may try a few rounds with a tight sling and see what happens.

My limited experience is that a sling makes for easier carrying whether on foot or on horseback. IMO, it also improves off-hand shooting. Some hunters worry about it getting hung on brush at an inopportune time, but I have not had that occur, and believe it unlikely if carried appropriately. It is possible that your grouping would vary using the sling vs. a rest. Just have to try it out.

I used bolt rifles exclusively for a couple of decades. Always used slings and can't remember ever taking them off. On a double, they just get in my way.
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"Serious rifles have two barrels, everything else just burns gunpowder."

I am a big believer in using a sling as a shooting aid, for a bolt rifle. If you plan to use one be sure and sight in your rifle while using it. You will probably shoot much lower at a distance when using the sling.

I DO NOT use one when using a double rifle.

Nor do I use one on a bolt rifle, if the sling attaches to the bbl as opposed to the stock.

PS I have seen 400 Nitro hunt with a double rifle... "He don't need no sling to kill pigs"... That is for sure.

I suspect the sling would change the impact on a double rifle..

I don't use slings on any rifle as rule. I carry one in my jacket to use if I am dragging out a buck or whatever...I don't hunt with one, and I don't shoot with one..I grab a rest on a tree or rock, shoot sitting or shoot off hand, and I always have my rifle ready to shoot. not hanging off my shoulder..I'm not recommending this, its just the way I do it based on my own experiences.