Am I able to upload the version of the project that a client is running?
There is a pending "Project update available" shown on the client, but I do not want to apply the update.
No, you'll have to restore the prior version in the gateway. (Even if you could, it wouldn't be complete: A Vision client doesn't retrieve an entire project while running--it retrieves the resources it needs, caches them until memory gets tight. Windows never opened wouldn't be retrieved by a client.)