If the site can control the extension, yes. Look at
If the site can't control the extension, no. Chrome protects the extensions.
But there are ways.
If the extension has
chrome-extension://oiplkfaidhjklglajdpfehoagkmlcakh/images/camera.pngfor Pig Toolbox) and check the reply.
If it is not an extension but an app, the site can just use
If the extension wants to check other extension, it can use