Details seem to vary by area, but yes - there were instances where matchlock firearms were loaded with paper cartridges. There were reports back into the late 16th Century of armies relying on paper cartridges for loading their firearms, particularly in Germany and Italy. By the time the 30 Years War rolled around in 1618, cartridge systems to easy loading would have been in regular use.

However, based the 1608 drill manual of Jacob de Gheyn and other extant drill manuals from the period, the preferred method appears to have been to rely on wooden - rather than paper - cartridges suspended from bandoliers. These appear to have been used in a similar way to paper cartridges in that they allowed powder to be portioned out ahead of time, but bullets and priming powder would be carried separately from the wooden cartridges. This here is a particularly good demonstration of the manual.

However, while this particular method is well documented, it's likely details differed between areas, particularly in futher flung regions like Japan and peripheries like Eastern Europe and the Balkans. I can't speak for those areas - modern demonstrations of Japanese Tanegashima matchlocks appear to use some kind of cartridge for reloading, but it's unclear as to whether or not that's something done out of convenience.

Apparently, paper cartridges started to become more popular around the time flintlocks started to come into favor at the end of the 17th Century, but unfortunately I can't find something as clear as the de Gheyn manual of arms and it's not my area of expertise so I don't want to confuse things with blind conjecture. Whatever the case, paper cartridges absolutely appear to have been the norm by the time the Napoleonic Wars rolled around, and by the time rifled muskets came into use by the middle of the 19th Century, paper cartridges had become the standard means of loading.