There are now a number of laws affecting this.
First is BATFE and its regulations.
Then you need to check ITAR and its regulations.
Then you have to convice ICE you are complying with all the regulations.
No. It takes an importer's FFL and ATF approval to import "military surplus" barrels. If it was a "sporting" barrel, you could get an 01-FFL to import it for you.