Yes it is feasible, but it wouldn't solve anything.
If a criminal used a stolen gun, it would imprint the SN# of the stolen gun on the spent cartridge. Brass catchers solve that - and the brass would only be tracible to the stolen gun.
If cartridges were imprinted with a SN# at the factory, the brass could be traced to the purchaser, but ammo gets stolen too and brass catchers would also solve that.
It doesn't do anything but raise the cost of ammo, annoy legitmate gun owners and force them to give up more liberty.
Heh! Revolvers don't need brass catchers. I see a renaissance in wheel-gun popularity with the criminal class.