Yes it can to some extent.
This is because the screen resolution gets larger and larger with each step.
Mostly you will notice a frame rate drop with PC games.
If everything else is the same as you go to next size larger monitor the frame rate will drop with screen resolution increase.
If everything is working normally otherwise I wouldn't worry about the spinning download graphic. All that tells you really is that it is working not the actual speed. It could just as well have a flag waving so you know it is downloading. Mike Sledge I was typing while you were posting.