Can improper GPU thermal paste application cause white vertical line on iMac screen?

What year model is the iMac?

Identify your iMac model - Apple Support

Chopped up screen sections and graphic anomalies, generally indicate an issue with the GPU.

Thin 1,2,3 pixel wide lines from top to bottom or side to side, generally indicate a display issue.

Take a picture of what you see on the screen and post it using the image insertion icon below.

That is a bad display panel or bad display cable connection, not a GPU issue.

Improperly installed thermal paste can lead to cpu overheating as heat is not being properly dissipated. An overheated cpu can cause various problems.

If you know it's improper or improperly installed or an insufficient amount was applied, redo it. I prefer Arctic Silver after a thorough cleaning of all contact surfaces.

The last time I saw that problem, it was actually the display panel that was bad.

What exactly do you want to know?

It sounds like you buggered something up, whether due to the thermal paste (unlikely - that should only show up after some use) or something else.