The Skippers Club is not a membership thing, it is a service that all suite passengers get regardless of whether it is their first or fiftieth Carnival cruise.
Although suite passengers probably have a better chance at getting invited, it is more likely to happen for someone who has cruised with Carnival a lot, regardless of their cabin level. Some Captains are more social than others. I've been on cruises where the Captain never ate in the dining room - thus there were no invitations for dinner with the Captain. I've also seen the opposite happen.