Interpret this as you will as far as being prohibited while an alien is in the US. Leaves kind of a grey area.
18 USC 921 Definitions
(a)(17)(A) The term “ammunition” means ammunition or cartridge cases, primers, bullets, or propellent powder designed for use in any firearm.
From another site:
Importation of Explosives
Canadian Law: Quantities that may be imported for personal use by a Canadian and not for sale without requiring an Explosives Importation Permit from Natural Resources Canada (NRCan) include:
small-arms, sporting ammunition, up to a maximum of 5,000 rounds;
primers, up to a quantity of 5,000;
empty primed cartridge cases, up to a quantity of 5,000; and
propellants, smokeless powder in containers not exceeding 4 kilograms and black powder in containers not exceeding 500 grams, up to a maximum total combined quantity of 8 kilograms, (17.66 pounds).
However, this is in conflict with US export laws.
A common belief is a Canadian who purchases, wins, or is given ammunition, primers, and/or powder can return to Canada with the items. This is not correct. If stopped at a secondary US Border Patrol checkpoint prior to reaching the border, at a minimum all such items can be confiscated.
The US govenment requires an export permit for ammunition or ammunition components (powder and primers). Permit required even if won at a shoot or given by a friend!