No, Wyndham doesn't offer status levels per se. The only trick is that you don't actually get any of the ByRequest benefits (free wi-fi, free calls, welcome snacks, etc.) until you've stayed three nights. Your account is automatically upgraded after that.
With Choice Privileges, Only the standard rooms and suites are available for award booking. Usually rooms with "premium" features (whirlpools, etc.) are blocked out. Presumably, one could get upgraded into one of those, but I've never had any luck yet.