Had there been a round in the chamber, would the pistol have fired or would the hammer only have struck the interceptor?

With no magazine in the pistol I pull the slide to the rear and release it.  The hammer is then in the fully cocked position.  I move the safety to the on position (red dot covered).

I insert an empty magazine in the pistol.  Again, with the safety apparently on (red dot covered) I pull the trigger and the hammer falls. It seems that if the hammer is cocked, and the safety on (red dot covered) the pistol should not fire. 

Wrong! STOP and refer to your OWNER'S MANUAL, pages 19 and 20. Confirm that your pistol is a "F" series pistol i.e.. 84F. Please see the included PDF document, including pages 19 and 20 of the owners manual, for your immediate reference.  In the question posed, the user is attempting to override the proper function of the Model 80F series pistol decocker safety and employ the safety in the manner referred to as cocked and locked, a safety system that is synonymous with many older designs of single action self loading pistols such as the US Model 1911 and FN/Browning Hi-Power pistols. The decocker safety system is synonymous with the Beretta Model M9/92FS and variants as issued to the United States Armed Forces and many law enforcement agencies. The decocker safety system was a prerequisite design feature required by the Joint Service Small Arms Program in an effort eliminate the potential of an accidental discharge from "hammer slip" that is inherent to the cocked and locked single action self loading pistol. The Beretta 80F series pistol utilizes a decocker safety system, this system does not function as a cocked and locked safety system. The owner's manual specifically high lights the correct function of the Model 80 "F" safety, twice on page 19 and once on page 20. For the correct function of the safety system: "FULLY engage the manual safety lever To Lower the Hammer and stop it against the interceptor."

Note that these three instructions focus on the following Key Words: "Fully Upward", "Fully Engage", and "Lower The Hammer And Stop It Against The Interceptor".  
IF your pistol is an "F" series and IF the safety is moved FULLY UPWARD to the FULLY ENGAGED position, the HAMMER MUST BE  LOWERED and stopped by the interceptor FOR THE SAFETY TO BE FULLY ENGAGED. If this is not the case either:
a) you have not moved the safety lever FULLY UPWARD or
b) there may be a mechanical malfunction,  immediately discontinue the use of your pistol and forwarded it nearest Beretta Authorized Service Center for inspection and repair.