I think the faster pixel response times of newer LCD monitors may make it look like websites load faster because the website shows up faster on the screen, and the rest of the website shows up faster as you scroll up and down a website.
Older LCD monitors have a slower pixel response time of 10 milliseconds while newer monitors have a pixel response time of 4 milliseconds or less. Some faster online web browser may look more smooth.
Screens in general have no impact on whether it loads websites quicker or not.
It's a display, has nothing to do with networking.
I think you're referring to the "refresh rate", which makes stuff appear smoother, but it's only really important in games and videos.
It's entirely unnoticeable in every other situation.
A monitor with a faster response time can change pixels to black from white or black or white according to a video I watch on YouTube. I think if you are on a very a fast loading website, and using a very fast connection, the text and pictures on a website may show up and load slightly faster.