But it does not answers my question. Talking about the adapter and not the cable.
In the old days when there were only two MBP adapters of different wattage, no battery damage but the rule was you could charge, or you could run the computer, but not both. That was the past.
Today there are so many different adapters that I doubt any of your fellow end users here want to stick their neck out to make such a blanket statement. I know I've changed my tune to "use only the correct adaptor" since the proliferation of different adaptors and connectors.
Again we're end users, not Apple, If you want a definite answer, you'll need to contact the Mothership.