You could register the gun and make it fully legal to use under the NFA in which case yes, you could possess shells and even fire them. There's paperwork, but it's possible and some people do it. Um, here:
(Making, say, a 50 caliber gun legal under the NFA is indeed somewhat more onerous than owning a shotgun. And a gun rights advocate certainly could care about trying to make it less so but they're not required to care about it because - as I said above - a tank doesn't count as "arms".)
https://www.dailydot.com/unclick/operational-tank-for-sale-a...
(Making, say, a 50 caliber gun legal under the NFA is indeed somewhat more onerous than owning a shotgun. And a gun rights advocate certainly could care about trying to make it less so but they're not required to care about it because - as I said above - a tank doesn't count as "arms".)