Yes - when the GPU is full power and the CPU is committed, you could drain things faster than the charger can provide. I’ve not seen it often, but you are certainly able to run things past what most chargers can provide.
Now if you can get this without any external displays connected and when the integrated (logic board) GPU is running and not past 75% CPU load, I would suspect you either have a bad cable, bad adapter or less likely need a repair on the Mac.
Now - one hour battery is clearly an issue. This draining should be slow and run several hours if you are running mostly on wall power and only a little on draining the battery.
Think if you were flying a plane and refueling - you should be topping off slowly or perhaps burning more than you can take in in some cases but you should be able to drain both your tanks and the refuel volume in an hour.
Get the Mac to service for a diagnostic on power with that specific adapter if that’s the case.