You can do that but it will limit your ability to make effects changes (eq, compression, reverb, delay, pitch shift...) to specific instruments and vocals after they are tracked. You can add effects to the whole mix after tracking or you can add the effects as you track through your mixer.
I would suggest tracking the drum kit through the mixer and into your MSR 1226 leaving you four remaining open tracks for guitars, bass, and vocals. Assuming you use the left out of your mixer as one track and the right out as the second track, you could track the Kick and Toms using one channel of the MSR 1226 and the snare and OH's using the second and so on.
Not going to have the versatility as would more track capability but it will be possible to get a decent recording if you are willing to experiment.
Good luck!
