Aside from the obvious that they can check the serial number in their system, the back of the 2g mini's have the capacity etched on them. The 1g do not.
I had to exchange a mini 2 times in about a week. The first time I did it in an Apple retail store, the next time I did it through the mail. I got a 1g back both times.
Apple probably has 10,000's refurb mini's they need to get rid of, so I wouldn't expect to be getting a 2g in it's place.