I'm getting ready to publish on Itch for the first time, and I'm publishing something that requires the XNA runtime.

I'm reading the docs that suggest I should upload an installed copy and list the prerequisite (rather than uploading the installer which installs the prerequisite too), and, this sounds great if the user is using the Itch app, but I can't find anything that explains what would happen if they were to download it through their web browser? Would a user downloading from the webpage just not get the prerequisites and be unable to run it?

The files downloaded via the browser are exactly as you packaged them. We don't insert any prerequisites. It could be an interesting thing to add in the future, but for now I recommend including links to the necessary things in the install instructions.