Well that does work sometimes. .38 S&W in a regular revolver is an example, but the difference in diameters is only .002" or .001" to the side. In a cap & ball conversion with a .38 Special cartridge, the .358" bullet may go into a .370" or larger barrel. That would leave a gap of .005" or more to the side. This isn't catastrophic or dangerous, but you may find you have grapefruit-sized groups, keyholed bullets and a badly leaded bore. Then again everything might be fine. All I'm saying is that it would be a shame to spend a lot of money for a cylinder, and then be disappointed in the revolver's accuracy.
Back before the Italians started making cartridge conversions as cartridge revolvers in the first place, serious shooters would have the barrel of their caplock revolver bored out and lined to get the right size bore for the chambers. This worked fairly well, but was expensive. When all of the associated costs were added up it was much less costly to buy a cartridge gun in the first place.
Many people have installed cartridge cylinders in their cap & ball revolvers, and seem to be well satisfied. Perhaps their expectations in the accuracy department aren't as strict as mine. All I'm saying is that it would be wise to determine what you're dealing with before you lay down any bets. The decision is up to you.