I’ve tried adding group places to my profile from both a group I owned and a group that I didn’t own but had edit permissions for, and I wasn’t able to add any game from either of those groups to my profile. I can add/remove my own games to/from my profile, whether they be inactive or inactive, which is great, but I can’t do the same with group places.
Edit: On a side note, “Add to Profile” enables us to do some really awesome stuff like feature items we want to sell, items by other people we want to endorse, limiteds we have for sale and hide/add places to our profile:

