A couple of things - it was mentioned above but if you wish wish to mix on the fly, you need to deal with the time delay between the sbd feed and the time it takes the sound to get from the PA to your mics. If you record onstage or very close to it, it's a non-issue, but the minute your mics are more than ~10' from the stage/PA, a noticeable delay between the two will be present. You can adress this if you mix them later on, but if you choose to mix on the fly, I wanted to make sure you understood this.
As for running on stage and getting your cables back to the sbd, if the band/house are agreeable, you can just plug your mics (assuming they are XLR) into the big "snake" that runs from the stage to the sbd and then pick up your aud feed from the sbd without having to run your own cables. There usually are always at least a few unused channels in the snake at most shows. I don't know what sort of band/music this is, but the onstage mics works better for some than others. Also, the aud source will only really be good for mixing and not as a stand-alone recording if there are vocals and/or instruments such as keys, horns etc. that are primarily only audible via the PA speakers (i.e. you can get a great recording of guitars, bass, drums but will miss the quieter stuff that are boosted in the house mix via the PA speakers).