Not all the way through, no. The base of the case prevents that. If the cartridge does not go in to the base or is very tight/gets stuck, that's bad.
Edit to add: just google plunk test for images and videos.
Using the barrel as a case gauge. Drop the round in the barrel (chamber end) the case should "plunk" in and out. Side note, people more knowledgeable than I might be able to tell you if your particular gun is known to have barrels on the smaller side.