Remember when Ian tells Edwin that club members either are kittens or lions (or tigers, I don't remember well)? Elias is a kitten.
Many club members look down on him: I bet that they will treat him like they treat Isaak.
IMO, inviting Elias is kind of a double-edged sword for Kat.
On the one hand, he's rich and could be a valuable member of the club, and if something goes wrong, the club owners have both legal and not-so-legal ways to put him in his place.
On the other hand, what if he snapped and tried to get back at the club in some way? Of course, he's just an arrogant rich guy compared to the other club members, but again, he's arrogant and narcissistic. Will his ego withstand the fact that the underground club of perverts mocking him for about a month, and his property (wife) sucking cock at stage?
About the same regarding Felicia's reaction to this. Her husband showing up can either motivate her to do ANYTHING Kat has in store for her (like, well, now your husband knows about everything and you have no choice but to win) or break her down (like, well, now that my life is ruined, screw you and your club, I'm leaving).
Plus, Elias clearly recognizes the "journalist" who interviewed him and who is banging his wife on stage, which puts Edwin at risk.
On the other hand, Elias' invitation confirms that Kat is actually addicted by her sadistic tendencies so much so that she's willing to take risks to satisfy her desires.