I'd say, "it depends." We upgraded 1.9 -> 2.0 -> 2.1 -> 2.2 ->2.3. Other than verifying the database schema before upgrading to 2.0, I did nothing other than run the upgrades.
Saying that, I have heard both that upgrading through the version as I did (it was 1.9 -> 2.0 -> 2.1 in the first of 3 upgrades) is best. And more recently, I've heard that it is best to first upgrade to the latest 1.9 release, then to the latest 2.2 release because (in theory) some upgrade issues have been resolved there compared with earlier versions, then to the latest 2.3 release. This second approach is probably what I would try if I were doing it today. I would test everything on a copy of your live site before upgrading the live site itself.
Note that the 2.3 upgrade specifically states that you must be at 2.2 first. I've heard of some few hacking the install to allow a direct upgrade from 1.9, but I'd say if it doesn't want you to do that, you probably shouldn't.
Also, you don't state your environment. Earlier 1.9 releases worked on php 5.2 and did not work on php 5.3, where 2.x releases require php 5.3 at a minimum. So depending on where you are currently, you may need to upgrade to the latest 1.9.x, then upgrade php, then proceed with the 2.2.x+ and 2.3.x+ upgrades.
But to directly answer your question: No, it shouldn't require a manual transfer of files.