Let me understand: Felicia herself stated why she joined the club, so we need to explain why she joined the club? Is it so difficult play the game, actually reading the dialogues?
To be fair, characters can and do lie. It's not unreasonable to evaluate independently whether their statements match reality as we see it.
What I find exasperating is that people insist her statements *have* to be lies simply because they disagree with her assessment of the situation. While I would rate the chances of Felicia's plan succeeding as very low (definitely lower than she rates them), it seems obvious that there IS a chance of it succeeding if everything breaks in her favor. We can have a debate about how good her odds are or what alternative options she has if we really want to, but I don't understand why it's so hard to accept that a woman who came from the mud fields to marry one of the country's more eligible bachelors might feel confident she could win over a few Club members if she can just get the right sort of access to them.
Eric (Police Chief) is a club member too, who respects him? Even Veronica fucked him over. Similarly Even when she becomes a club member (if she wins) she wouldn't have anything of her own and she would still be an invaluable trophy wife without the so called important information (the importance of which wouldn't change if she is a club member or not) that she has that (I will say it again) she could have used to her benefit if not easily then with a little bit of effort, if she would have been a real person she could definitely make anyone listen to her without joining the club with a little bit effort and her contacts.
The fact that there might be members of the Club who don't respect her membership isn't the right benchmark. The key issue is if there might be members who WOULD respect her should she become a member. Given how Chuck has reacted to her thus far, I think the answer to that question is at least potentially yes. Would that be enough for her? Hard to say without knowing more about what she's planning, but it would give her some resources to work with.
Also, the chief of police is Jim, not Eric.