This question has been answered by carlo_13. See the first response.
What's happening during or after upgrading? Are you getting any errors or white screens?

It works for me.
On the rare occasions when it doesn't work, it doesn't seem to do any harm since it quits before downloading the new files.
If you already have the files in place, though, I'd recommend disabling your plugins and re-running setup. The blank screen suggests a plugin that's interfering with Setup.
If you try to update straight from 2.2 to 2.4 you website will break.