Doors will still be a huge hindrance for homunculi even if they can open them. It will presumably have a long homunculus balance cost (since everything else does, even just checking the exits in their room), and failing to move because a door is in the way still costs 5 seconds of balance.
I can't really see why not. You can probably count on one hand the people who bother moving their homunculi all that much in the first place, because of the prohibitive balance cost.
And you won't understand the cause of your grief...
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And you won't understand the cause of your grief...
...But you'll always follow the voices beneath.