Like Michael suggested, if you do that, transcode to DNxHD for Avid creative editorial. Then conform from the APR originals on whatever tool suits your needs for finishing. In MC/Symphony-Mac, you could relink the cut to the originals via AMA, flip the project to RGB709, and then try to stay ProRes all the way from there.
If you stick to APR in Log-C during creative editing, everything will indeed look washed out, milky, soft. If you color correct your cuts, you can get a nicer picture, sure, but all source footage (when loaded into the source monitor) will have the milky look. Very uncomfortable during editing and obstructing to work around when reviewing/comparing takes. And that’s a biggie to editors, producers, and directors, let me tell you that from experience.
Plus: transcoding is fast, and since you have to somehow bring the footage into Avid (you don’t want to AMA-link to the originals for anything you’ll be working on for more than a day or so), then why not bake in a LUT while you’re at it?
And a pet peeve of mine: note that in this day and age, editors are expected to constantly adapt to new workflows for new formats, and they often manage that just fine. Now it’s nice that you prefer an all-APR-workflow, but do realize that your editors need the right conditions (like proper looking images) to work their magic on your film. If that means an hour of transcoding time per shooting day, that should be manageable, in my opinion.
Hope this helps.