What you really need to do is to transcode all the Video to OP-Atom DNxHD in Resolve and then Resync everything in Avid. If you change the timecode of the Audio and transcode from Resolve with Synced Audio the Video Editor(s) won't care but the Audio editor(s) will have major issues with this.
After the Video edit is done the Audio Editor(s) will need to link back to the original Audio in many cases and if you adopt your suggested workflow they won't be able to do that. First, you really should never change the timecode that's embedded in any file and second if you transcode the clips with the synced audio any reference to the original audio will be lost. Linking back will be a nightmare or impossible for the Audio Editors. I've worked with FCP-7, X, Pemiere Pro and Avid but never have I synced in a different NLE than the edit is going to be done with, that makes no sense whatsoever.
Not using timecode is a massive error on everyone's part on a project like yours but if that's the way it's going to be then the only other option is to send a mono audio mix to each camera. Even if the cameras do not have T/C Inputs, products like Tentacle that send T/C to an audio channel are cheap enough to buy or rent and will save everyone from days of frustration, delays and money in the end. If you go the Audio route then you can use the Sync by Audio Waveform feature every NLE now supports and again save, save, save.
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