Hello Curt. I have not studied geese genetics in enough detail to be certain (book learned but not verified in real life breeding) and therefore I'll post my answer to your question in public so that if my understanding is incorrect, someone can chime in and correct.
You asked if one could produce showable offspring by crossing a Buff African male with a Brown African female.
It's my understanding that the only difference between the two varieties is a single gene, the buff gene. Therefore the cross should produce buff females and brown males (which carry the buff gene). The Males would be showable as Browns and the females showable as Buffs. However, the APA only recognizes the Browns.
I would love to have offspring from this male as he has nice orange feet. Most of my Browns have feet that are closer to pink than orange and the standard calls for orange feet. I see an opportunity where we could help each other improve the variety, especially if your female is the one that hatched on our farm.