I do not use Download Manager so I can't comment on that method. Someone who uses Download Manager should be able to give you an idea of what to expect since the patches are downloaded and applied outside of a regular Patch connect.
If you are NOT using Download Manager, patches are downloaded and applied during the Patch connect, and Patch compliance data is sent as soon as the Patch connect ends.. In my lab it takes a minute, but in a production environment it will depend on several factors but should be visible in under an hour in most cases.