In short...yes
Corgi's have bad backs as well-same reason likely-loooong backs
However Corgi's make super agility dogs. So do doxies
YouTube - Dachshund agility, first Excellent B (Standard) first placement, 2009 04 05 Vero Beach
You'll want to use precautions (and agility regulations have rules about how high a dog is=how high the course is)
No jumping down from or over anything taller then they are-at shoulders
No obesity
No agility until they are done growing.
BUT yes yes yes good exercise good stimulation good challenge good bonding experience

Know your dogs limits and abide and I see no problem