Yes. The RSVP and booking forms work on cached pages. Each form fetches a fresh anti-spam check when the visitor first clicks or tabs into it, or at the latest when they send it, so a cached form never expires. The seats left on a cached page can lag behind, but the real count is checked at sign-up.
For a signed-in visitor, a page with a form holds a security code tied to their account, so HappenBoard asks caching plugins not to store it.
Behind Cloudflare, another CDN or a reverse proxy (a relay server in front of your site), every visitor can seem to come from one address. Real people can then be refused with “Too many RSVPs from this address”.
Ask your developer to pass the real visitor address to HappenBoard. The code is in attendees and sign-up hooks and appointment booking hooks. Protecting your forms from spam explains these limits.