All film SLR cameras have a mirror that swings up out of the way when the shutter is pressed. DSLRs may not even have a mirror, if they're using an LED viewfinder display rather than an "on top" traditional (through-lens) viewfinder. Vintage lenses (for SLRs) would be designed not to interfere with any mirror behind them, which should not be an issue if there is no mirror. The shutter is usually a curtain mechanism in the body (behind the mirror). My concern would be that the mount is compatible, not only securing the lens to the body, but also "passing through" any functions or settings between the lens and the body that it is supposed to.
Probably your best bet is to enquire of someone authoritative (camera shop expert, lens and/or body manufacturer) whether those lenses will work with a given DSLR camera. And get a money-back guarantee if it turns out your lens doesn't work with it. All of these are complex mechanisms, and it's a good chance that just reading websites won't do the job.