To read data from another URL and analyze it is possible to create as a WordPress plugin. However, very little of the actual code in the plugin would be WordPress-related.

Does the Kissmetrics site ACTUALLY analyze your site? Or is it "identifying improvement opportunities" and requesting you email for more info? (Neil Patel does this; if you enter the same URL twice, you'll get different results from his "analysis".)

So the short answer is yes. Medium answer is that it's not going to have much to do with WordPress. Long answer is that the function you're looking to mimic might actually just be marketing smoke and mirrors.

If you'd like to get a full technical breakdown of how the plugin can be built, I'd be happy to work through it with you. Request a call and we'll set it up.

Good luck!