Yes. If referrer is enabled then the referrer information in the http header would have to match your domain. With the referrer check disabled the http packets could come from any site.
Keep in mind that using a referrer check is a deterrent, and not a guarantee. You could still get spammed by another domain even if you have the referrer check enabled because the referrer information in an http header can be spoofed.
So far I haven't had a problem with someone spamming my board. Since Threads does a pretty good job of recording the source IP address that was used for a post most people don't bother. You would have to use some pretty sophisticated scripting routines to make a spam post and spoof the IP address that you are coming from. Not impossible, but beyond the means of the average "script kiddy" hacker.
The best security advice that I have is for you to force people to give you a valid email address so they can get their initial password, and allow mods and admins to see IP addresses. You could even block email registrations from free sites like hotmail and yahoo, and any site that acts as an autonomizer. People are less likely to get out of line if they have to give you an email address from their ISP or a work email server...
