Depends on the state of tune, strength of spring, and a bunch of other variables. Early SUs had no dampers at all, nor did they have springs, but the piston was heavy and didn't tend to oscillate much. When springs were introduced, the dampers' job was literally to damp their oscillations, not to act as a spring themselves. So you can run a dry SU with a strong spring and mitigate the acceleration stumble that Banjo refers to.
However, I do suspect that some owners check far too often and overfill their SUs and Strombergs, too. In the SU case in particular, there's nowhere for the oil to go and it won't evaporate quickly. So folks fill 'em up, then when they check again, there's less oil so they fill 'em up again. In fact, part of the problem is due to vehicle manuals being wrong. They indicate far too high a level! Once you fill an SU, then replace the damper, then run the engine to WOT, the oil level will end up somewhat below the top of the hollow damper tube in the piston, and that's where it should be.