Patrick, I do have to ask, where is the "piston" on a M1861 Rifle Musket?
And ncblksmth1, the answer is an empahtic "No!" The breachplug is never removed unless serious repair is required and then should only be done by an experienced gunsmith. The gun can be more than adequately cleaned with the plug in place.
Also, what are the markings on your lockplate?