Police don’t really give a rats and doubt they make an effort to stick it in a database if you report it stolen. However they do use and promote Immobilise to check for property owners should they find things. https://www.immobilise.com/
I’m wary about registering things in advance on it though. Always a chance the site gets hacked and then they’ve got a massive shopping list with addresses on it.
Keep all your details, serial numbers, photos etc yourself, and if something gets nicked, then register it.
Slight concern I’ve got for a public FB group is while it’s a great idea for recovering stolen items, it could also be a great idea to note down who’s had what nicked and if they haven’t been careful, where they live, then sit back and wait for the insurance replacement then nick that.