Depends somewhat on calibre, and load combination as to where the first shot goes. Long time ago, I knew of a fellow down 'South' in BC, who loaded 10gr. more for his first shot than for the load his gun was sighted for. He said the extra 10gr. gave him back to loss of elevation his first shot normally gave.
Problems arrise when the first shot is not only high or low, but off to one side. This side shooting is more common to modern rifle ctgs. due to the gross vibration and barrel harmonics they produce, however a long whippy ML barrel can give the similar results. I know of fellows who mainly hunt and therefore sight for the first, clean barrel shot.
Others fire a fouling shot. Firing a fouling shot before hunting means the gun must be cleaned that day- ie: the load discharged or pulled at the end of the day then cleaned. We found some guns did not like to be carried all day with a load over a fouled bore and breech ie: mainly some cheaper production rifles gave ignition problems when this was done - the normal hunting temperatures of -30 to -40F might have had something to do with that.
Back then, in the late 80's, I was hunting with the .69, a 14 bore rifle Taylor built for me. I found the difference between the first clean shot and the successive 'fouled' shots was not noticable on target, even at 100 yards - wonderful - I could leave the clean rifle loaded almost indefinitely and still hit centre with the first shot. Carrying a charged, but unprimed or non-caped Ml in a vehicle is legal here.
If there is a BIG difference between first and successive shots, one should find if that difference is repeatable, and if so, learn how to hold for it. This means one would actually have to shoot his gun enough to find out - and then take action - pretty easy to do, actually.
My current 'trail' rifles, a .32, .40 hit centre at 25 yards with their first, clean bore shot - which means they also hit centre at 50 yards. There might be a difference at 100, but neither would be used on game at that range. These guns hitting centre with a clean barrel might be due to something as simple as using a tight enough combination that the 'dirty' bore is little different from a clean bore. I don't know if that is the situation, but do know different points of impact don't bother me with those rifles. For me, a 'fouling' shot at the start of a trail walk, is merely a practise shot as the accuracy is the same, 1st, 2nd or 50th.
In the .32, I shoot a .311" ball with either a .0215" ticking or .0225" denim patch. It loads easily with the 5/16" hickory rod - all day- no wiping.
In the .40, I shoot a .398" ball with the same patches. The bore is .398". I also use a .400" ball with .019" drill patch. A 3/8" hickory rod is used for loading - which is quite easy. Either mink oil or minus 40degree windshield washer fluid with a couple ounces per quart of neetsfoot oil or spit is used for lube. There seems to be no difference in fouling over a day's shooting with any of these lubes- other than, the mink oil feels a mite slicker when loading. My .45 longrifle is different in that it hits 1" high at 50 yards with the first, clean barrel shot - possibly due to it's longer barrel's harmonics. The difference is not enough to be important under most situations, certainly not deer hunting or on trail walks.
The reason I mention those loads is to illustrate that 'snug' combinations (at least in these rifles) seem to shoot the same or similar, clean or fouled. In this scenario and due to the tight combinations, 'fouled' is only a word barely a description as the bore seems to get wiped very well when pushing down the next patched ball.
When cleaning a barrel after a day's shooting by flushing water in and out the vent in a 3 pound coffee can almost full of water, leaves the water barely greyish in colour. This is after firing 40 to 80 shots without wiping at any time during the shooting or before cleaning. The greyish colour of the water comes mainly from the builtup fouling in the powder chamber area and vent cone, as there is litterally only the final shot's fouling in the bore. This happens whether we're at Rendezvous BC (Hefley Creek) where the humidity is 6%, or when shooting in high 80 to 90% humidity - there is no difference in fouling or points of impact.