Will "backup -> factory reset -> restore" free up space?

Your suggested backup/restore process will only provide a temporary respite. Caches will be cleared, but they will regenerate.

In iOS 11 Settings > General > iPhone Storage will give you recommendations as to how you can free up some space.

You can offload apps (delete the app but leave it's data, settings and icon) and you can store your photos in iCloud.

You can process your photos using something like JPEGmini or Half.app and regain some space.

But really you're fighting a losing battle. I recommend you upgrade to a larger capacity iPhone so you don't have to waste time and energy on keeping things just below capacity.

This answer may not be very helpful as I cannot give you a definitive Yes or No, but my guess is no. After a google search I found this, and since at least voice memos probably get synced to itunes, I assume there is other stuff in the 'Other' category which gets synced as well.

I once needed storage on my old iPhone 4S though, and clearing cookies helped. Be careful what cookies you clear though, some could be documents you worked on or something. Most of them, however, are just keys your browser and the website remember so you can tell the website them and you don't have to type in your password every time (not the same thing as saved passwords in browser) in other words they're when you close the window and reopen the webpage you'll still be logged on. Article on how to clear cookies by apple here.

A tip that has worked for me several times was to rent a (very large) movie in the iTunes store directly on the phone. Your phone will try to make as much room as possible for the movie, but if the movie is really large, this will still not be enough. So the rental will fail and you have a lot of free space.