Corporations can own all sorts of property, everything from fleets of trucks to stadium skyboxes, to downtown apartments for hanky-panky, so why not a TS. You will likely need a BOD resolution authorizing the purchase, corporate officer signatures and such, but its not really any different from any other R/E purchase.
Bear in mind that, if you intend to finance the purchase (not a good idea), the lender may not want to lend without someone's personal liability. Also, bear in mind that the directors have a fiduciary responsibility to shareholders (if its a closely-held corporation, they are likely to be the same), so... Buy "resale," and NOT directly from the resort or developer.