Using the sling fitted to one’s rifle is indeed a good way to support the rifle in the shoulder, and by tucking the supporting arm around the sling, one can brace the rifle and, to some degree, stop lateral movement.
The problem on a sporting rifle is that one usually has a more slender barrel and fore-end for fast handling and lighter weight, as opposed to the configuration of a service rifle.
This can cause problems if you want to use this method of sling support because, on a light sporting arm, it affects the tension on the fore-end.
As you brace the rifle in the shoulder, if the fore-end is slender, be it wood or synthetic, it can bend, and this often causes a change between the barrel and the fore-end as the rifle is fired.
The result is a change in barrel harmonics which will alter the accuracy and point of aim as you fire.
The effect is worse on a free-floating barrel that suddenly has the fore-end touching it, but fully-bedded barrels can also be affected.
To see if your rifle is affected by the sling method, test it on the range.
You will find that shooting off sticks is often the better option when deer stalking.