Ideally having thousands of images in the thumbnail panel shouldn't slow down SC.
For example, I have 1000+ images in my thumbnail panel (screenshot directory) with no noticable slowdown.
But it seems there are definitely cases where it does -- I'm not sure if that's because of antivirus software, or windows thumbnail settings, or extensions, or some combination of factors.
So if you do notice a delay when a new screenshot is added, I guess it pays to try moving out the old images and seeing if that speeds things up.
You'll find one-time manual command to move older screenshots to a subdirectory in the MoveTo menu, and you'll find a setting for automatically (regularly) filing old screenshots into subdirectories based on date, on the "Saving and Loading" files tab in options.