Exactly! This is what the founders intended.
Well almost, they had privately owned cannons, and even cannon armed ships. The power of Congress to issue letters of Marque wouldn't make much sense if private individuals couldn't or didn't own those cannon and ships. You can't "bear", in the sense of "carry" those. But you can "keep", meaning own, have, possess, etc, them.
It was those cannon that General Gage's Redcoats were after on April 19, 1775, although his orders told 'em to take whatever arms they could find, including privately owned ones, as well as powder, ball, shot (for the cannons) and other stores such as tents, food, etc.
They didn't get the cannon, although they managed to destroy the carriages which were left behind, and they through some of the balls into the mill pond (where they were recovered later) and they got even more of the balls...the hard way.