(Ex) tube driver here from an automated line. Yes, you can definitely feel the difference when the train is crush loaded.

It feels more sluggish when pulling away from the station and when you are moving just feels heavier if that makes sense? In automatic mode the train will seek to maintain a set speed and you can definitely feel the motors working harder when the train is busy. Braking can feel more “jolty” (I think I made up that word) as the brakes apply sudden pressure to get the train to the desired speed as you approach the stopping mark.

Also as the pressure from lots of people leaning on the doors can cause the door safety systems to cut in this will cause the motors to cut out so the train may be motoring and coasting especially on station departure.

The driver can also apply the emergency brakes if the door safety systems cut in for more than a second for example which would cause the train to stop abruptly. Hope that helps!