Has the Naples Hotel been rejected as a possible site for the Naples Little Club?

The following is from an email I received from a friend that has provided the majority of research I've used to attribute many of my previously unknown c&s.

It's possible the club may have been located in the Naples Hotel.
At the time the chips were ordered (11/1923), the hotel was the center of social activity in town and catered to the wealthy winter birds who
flew in for the season and then went home (about the only way to get there was by boat--no paved roads to Naples or trains).

At that time (just before the 1923-24 winter season was to begin) there just wasn't much infastructure (or just plain structures)
in this small town and the Naples Hotel seems to be the nicest place there. A new manager, Peter Schutt, was hired in the
summer of 1923 and made some big renovations (maybe he ordered the chips). The following summer and into early 1925 the hotel made major additions,
including a new club room (it had a billiard room as well). Shrutt went on to manage the Casa Marina Hotel (now Resort) in Key West in the 30's, taking over from his
father, who was the original manager.

Naples Little Club at the Naples Hotel....

The following is an ad from Jan.1925 and a pic taken sometime after the additions of 1924-25.