Just curious if anyone has tested this

Nope, she counts like a regular companion, so you lose the effects of the perk while she is with ya, luckily you can use robot mods to give her silly amount of carry capacity.

Unfortunately not. Nor do your other robots

Ive tested and it doesn't work that way. I think Dogmeat is the only one in the game that works that way.

Well how else would it work, since some of the things the perk lets dogmeat do are specific to a dog??

These robots are more useful and powerful than any other companion in the game, it wouldn't make sense to have a perk that is supose to help you when you are alone if you are actually with the greatest companion in the game. I think allowing this would totally ruin the purpose of the perk. Dogmeat svcks as a companion and dies to everything.