GUN uses a proof of work for account creation/login I think, but otherwise no there is no proof of work requirement for updates.
I added the proof of work requirement to votes as part of my own validation. The difficulty at https://notabug.io is set quite low, but https://dontsuemebro.com is a peer that still has it set quite a bit higher, it rejects the cheaper votes at notabug.io so the scores/sorts are different.
Spent a lot of time focusing on performance, notabug.io is running GUN with redis as a storage adapter and doing server side rendering to speed up the user experience.
Domain pages are currently all gun/clientside though with out the server doing anything special to help at all.
https://notabug.io/domain/youtube.com/
Also when using the infinite scroll feature or chat most all content is loaded directly through gun without intermediary REST calls.