The answer to this question, in a single simple unequivocal no-part-of-which-can't-be-misunderstood word, is no. You’re not entitled to sign-up benefits for non-members if you’re already a member of a players club.
And there’s not much you can do about it, though here are a few ideas.
For one, as Jean Scott wrote in The Frugal Gambler, you can purposefully not join a players club until it offers a sign-up promotion of which you’d like to take advantage. She adds the caveat, however, that you might wait a long time for that promotion to arrive and meanwhile, you could be missing out on good playing conditions, which include promotions aimed at members.
For another, you can arrange to have a friend or partner who’s not a member sign up for a players club that’s offering a good promo. In the case of Hooters, for example, where new members get two tickets to Bobby Slayton or Gerry McCambridge, the second ticket would be yours.
Similarly, in a loss-rebate promo like the one offered at Arizona Charlie’s (and off and on at Harrah’s and other casinos around the country) where the casino refunds a new member’s first $100 in losses, you can go partners with the new member on the free shot.
This is a good reason to always sign up for an individual players club account, rather than opening a joint account with your partner. With individual accounts, you can sign up for a good promo like the 2-for-1 Hooters deal, taking your partner with you to the show on the coupon. Then, when another good promo comes along, your partner can sign up and take you. (This could also be an argument for switching out partners on occasion, if not regularly -- for instance, when your partner has finally signed up for every players club you belong to.*)
Furthermore, on occasion, some clubs put on "buddy" promos, where members get points or prizes if they show up with a non-member who joins.
Bottom line, though: Limits are limits. Unless otherwise specified, a 2-for-1 coupon cannot be redeemed for 50% off by one person. Room offers good Sunday through Thursday only aren’t honored on Friday or Saturday. If a local ID is required for some deal, out-of-towners aren’t eligible. And though it might hurt not to be able to take advantage of it, if you’re already a member of a players club, you can’t get a new-member benefit.
* Just kidding about switching out partners.