Nope. In order to start sway while running the nvidia driver you must run

   sway --unsupported-gpu

If you try to run it without that option it silently fails at any login screen. If you run it at the console you will note it TELLS you to run it with that option. This means the developer has detected what needs to be done to start a session and is silently telling you to go fuck yourself. There is no argument that every distro ought to exec a wrapper script that tests if you are running nvidia and if found pass --yes-I-understand-fuck-me-sideways when the net effect would be to replace the body of the if statement that already exists in the devlopers code and more to the point I don't think anyone has. You may note here is the default desktop file as provided by the project.

https://github.com/swaywm/sway/blob/master/sway.desktop

This is what everyone is using and it is exactly as broken by default as I claimed.