Enter a URL
This is another great tool offered by SuperSiteTools that captures screenshots of any website or web page.
How to Take a Full-Page Screenshot Without an Extension
Go to Supersitetools.com
Click on Website Screenshot Generator Tool Icon.
Enter your desired URL in text field "Enter a URL, for example https://google.com.
Click on submit button and download screen shot.
So, in this sense, the answer is no; websites can not detect user activities like capturing screens. However, if the website you download any software and install it, it can most probably recognize external screen capture tools being used on their web pages (if they want to).