Yes, that's likely much cheaper than loading up an aircraft carrier with a bunch of Mustangs and Silverados. They're still likely bound to some sort of lowest bidder for contracts. It's also likely to be more economical than having the person find their own transport and reimbursing them.
There are some pictures of aircraft carriers loaded with civilian crew cars, but that's when the carriers home port changes, so it does the trip anyways.
OK, but maybe they plan to use the same group of commercial shippers for the miltary hardware. (Now you are going to tell me that most of these shippers are Chinese, completely demolishing my conjecture.)
If its an American to American port, the Jones act would mean an American shipper. I'm guessing they would use Chinese if it wasn't though.