Coming back to report my experience for future reference.
I tested going from version 1.18.7 up to 1.50.1 and it was actually possible to go straight from one to the other, i.e. install 1.50.1 and let FA automatically upgrade the database.
If you are using custom themes, many new templates have been introduced and will be missing. A small issue that will come up in this case (specifically after version 1.37) is that the index page will be broken. This is because a new index template has been introduced and will now be missing. You can circumvent this by either appending "?bypassTheme=true" to the URL, or going directly to the login page "/admin". You can then login and fix any theme issues through the dashboard editor.
Another issue I faced was that for some reason (didn't look into it), any changes I made to my custom themes would silently be discarded. I had to duplicate the default theme and start from scratch. Given the many differences and depending on your use case, this may be a good idea anyway.