Yes the USPS can tell how many times that you have tracked a package.
The USPS tracking is uploaded and stored on web servers in a massive building called a data center and the USPS has server admins and IT people working on those servers and making sure everything is working correctly.
The server admins and IT people have access to the server logs and other information that make it possible to see how many times you have tracked a package.
Your IP address as well as the browser and device are all tracked and logged in the server logs and stored for awhile for security.
However the USPS does not really care how many times you tracked your package and they will not look into the information unless there is something bad going on.
So yes while the USPS can see how many times you tracked your package on their website they really don't care how many times you actually did track your package.
But all you need to really do is track your package every 24 hours because the USPS tracking is not updated in real time and the package will not be scanned for another 24 hours or until it gets to another sorting facility or your local post office.
Most times the package is on a truck or plane traveling to it's destination.