It's usually not at the application level that you have to worry about these things. The application is programmed to receive and manipulate data in a standard way. The manufacturers of the cards write drivers that interface their cards to the OS. If the drivers work, then any audio application in that environment should work fine.
The mixer has no interaction with the software at all. Audio devices are all made with standard interfaces -- XLR jacks, 1/4" jacks, whatever, that all present standard signal levels to the world. So if the equipment is all designed properly, any mixer would work with any soundcard as long as you could get the cabling between them worked out.
For what it's worth, I've been using a Delta 66 with Cakewalk SONAR and its predecessor, Cakewalk Pro Audio, for about six years, with no troubles at all. (Plus I have a Behringer mixer as well.)