The Audigy is a "modern" card so the joystick port is unlikely to work in DOS. Even the earlier SBLive needed special emulation drivers to work in DOS, which I think they stopped supplying with the Audigy. So as far as DOS is concerned, you will only have one card - the Audigy will be invisible.
In Windows, I'm not sure how the modern joystick port works but I suspect it won't use the same fixed resources they used to. So you will probably find that both joystick ports will work at the same time.
Sorry I was assuming when you said two sound cards that they were both older DOS-compatible cards. Since the Audigy isn't DOS-compatible (as far as I'm aware) then there should be no conflict between the two.