You can run them in the event but the points will not count towards an HRC title unless registered with the UKC, they give you a set period after running to get the UKC registration to apply the points. After that time you have just run for the fun/experience.
Make sure you get what the UKC calls the pink slip from your judges if you pass the test. If you want your passes to count toward a UKC title, the UKC requires you to register your dog with the UKC within 60 days after you pass your first test or the pass doesn't count. (Unless you pay a $50 fee and also pay the fees for registering the dog.)
One of my AKC registered dogs ran UKC without being registered with UKC. I then sent his pass slips when I registered him with UKC within 60 days and he got his title. BUT I lost a pass/pink slip for one of my other non-UKC registered dogs and when I did register her with UKC, her pass didn't count because I lost the slip. So remember to get the points receipt/pink slip from your judges and keep it!