It is well known that cleanliness is next to Godliness. When it comes to firearms, it certainly behooves the owner to follow a proper cleaning schedule, lest the firearm fails at an inopportune time or at the worst moment possible.
Some barrels are prone to accumulate powder residue and/or smears of the bullet or its jacket along the bore. This blight plagued the 357 Magnum in its infancy, when prodigious charges of powder were pushing lead bullets at velocities unheard of for a handgun. Within a few shots, the accuracy would degrade as the lead fouling would start to build up. In the case of the 357 Magnum, the use of jacketed bullets pretty much solved the issue.
Unless the bore of a handgun is especially rough, copper fouling should not become an issue, especially at the distance handguns are usually engaged and their reasonable accuracy expectations. Rifles are another story. As bullets zip through the bore much faster in a rifle, the friction and heat are likely to encourage bullets to shed weight along the way. These smears create an irregular bore surface for the following bullets and diminish their accuracy. Cleaning copper fouling will get rid of the issue, but it is usually not a walk in the park and involves a lot of sweat and aggressive (and sometimes downright toxic) chemicals that can hurt the gun or the person cleaning it. Some powders include copper removing compounds in their formula to reduce the fouling issue, particularly in high volume shooting. Whoever thought of that deserves a statue.
The opposite can be true as well. Some people have rifles that shoot better with a “seasoned” barrel. The posit behind this is that the manufacturing process of the barrel may have left tooling marks or some type of imperfection that negatively impact the accuracy, and that shooting a certain number of fouling shots help fill these areas with carbon, lead and/or copper residue, smoothing the bore and restoring accuracy. A gentleman I know shoots long distance matches with what he describes the “most horrible barrel he ever saw though a borescope”. He makes sure he shoots 30 rounds after a cleaning, and he is back at shooting quarter-MOA groups for 200 more shots before the fouling starts to negatively impact the accuracy.
The Weatherby Vanguard mentioned earlier can add that malady to the long list of the ailments it suffers. In my attempts to get it to shoot accurately, I would maniacally clean its bore before each session at the range. The groups would gradually improve the first 20 shots and stabilize after that, sadly, still far from the sub-MOA guarantee. Looking at the bore with a borescope revealed an impressive collection of abominations, especially for a supposedly cold hammer forged barrel. Longitudinal and perpendicular hairline cracks or marks, burrs and chattering were found pretty much throughout the length of the bore, but the most offensive violation is from a land that narrows and expands along its length, and has the bullet facing edge slope in places. After one last good cleaning, I was able to see how much material from the bullets were filling in these spots, likely bettering the accuracy to some degree.
While cleaning impacts accuracy, it also impacts function. It is critical to clean your gun to at least that degree, especially if you rely on it for your defense. Some guns are more tolerant than others, but I doubt there is a good time to find out about it other than at the shooting range.