Agree, mostly.
I don't know if "obey" is the correct word. Although, I'm not saying you are incorrect because there is the parent/child dynamic in play.
To intercede is "the action of intervening on behalf of another."
There's no doubt that Mary was intervening on behalf of those who were in need of more wine. That is intercession by definition.
There was a need, she knew the solution, and she took that need to the source of help on their behalf.
Again, I'm hesitant to say "obey" but there's no doubt that she influenced the subsequent action(s).
She then said, "Do what He says.." once again pointing to the source of help.
This is still the model for her intercession even today.