No. To. comply with US laws they cannot ship a firearm to a private individual.
In the US any gun you purchase must be shipped to someone who holds a Federal Firearms License (FFL).
Most FFL's charge a fee in the neighborhood of $25 to complete a transfer.
So to comply with US federal laws you must physically drive your gun across the border yourself.
Also purchasing a firearm in the USA with knowledge that it is for someone else is considered a straw purchase and it is a felony.
"In the context of United States federal gun laws, a straw purchase is defined as any purchase from a dealer holding a Federal Firearms License where the buyer conducting the transaction is acting as a proxy for another person. The law does not distinguish between someone who is purchasing on behalf of a person who legally cannot purchase or possess a firearm, and one who is not."