This will definitely work, however, you will be stuck with the mix you have. Since you're taking multiple inputs and sending them through the mixer and into a single channel on your interface, you won't be able to go back and set the volumes for different microphones differently, or add any plugins/effects to single microphones. Because of this, you will probably need to do a lot of experimenting, recording with some settings, listening back, making adjustments, and repeat. I've seen some people accomplish a great sound with this approach but it is very limiting since you can't adjust individual mics after the fact. With the 2i2, you should have two inputs, so I might recommend experimenting a little and choosing a microphone to send direct to the interface and allow you to have a little control over it after the fact. This would most likely work best with your kick or snare mic. Depending on your mixer, you may be able to create a couple groups of channels and send them separately to the interface, allowing you to separate some of the mics from each other.