Yes. I have an old French MAB pistol with a 0.309" bore in .32 ACP, the commercial ammo for which are all jacketed 0.311" bullets. It has no problems. In the worst extreme, a few careless persons have fired next-caliber larger bullets in rifles by forcing the case in until the bullet was seated way down in it. They got high pressure signs, but the only gun bursts I've ever heard of were in WW I with low number Springfield rifles that soldiers had, in the fog of war, picked up and chambered 8 mm Mauser cartridges in. But there are concerns about the metallurgy being bad in some (not all) of those rifles.
With the .45 Colt, especially, it went through a change in spec somewhere around WWII. The old bullets were 0.454" diameter, and the new are, as you know, 0.451". So, for a long time the chambers were made up to about 0.4560" to accept the old bullets, even oversized cast ones, while the barrel groove diameter was 0.451". I gather that is no longer automatically so, with SAAMI putting the throats at 0.4520" to 0.4595" and bullets at 0.450-0.456", but it does illustrate that guns can swage a bullet down several thousandths without a mechanical failure. Just work your loads up starting with the very smallest loads listed, while watching for sticky case extraction.