I'm by no means an expert on caching, but often find myself debugging cache-related issues in the client. My understanding is that the browser caches files based on the URL being requested, not the URL your browser is currently on.
E.g.: if your CSS request in your HTML page is to: test.example.com/app.css, and if that's the same regardless of whether you're on test.example.com?variousGetStuff or test.example.com?otherGetStuff, and assuming you don't have your browser set to not cache requests, and assuming your server isn't setting a no-cache policy on that file, then yes, your browser will likely cache it client-side.
You can actually test this yourself with Chrome's devtools— open it, switch to the Network tab, ensure the Disable Cache checkbox at the top is unchecked, then refresh the page. Find your .css network request in the list, double click to open the details, and check the status near the top. If you see 200 in green and next to it: (cached) in grey text, then Chrome's retrieving that file from its cache.
Hopefully that helps!