This reminds me... In an episode of "Mork & Mindy" Mork (played by Robin Williams) actually met actor/comedian Robin Williams. IIRC it was simply brought up because Mindy (finally) noticed the resemblance.
Another non-Trek example is that I've often wondered what comicbooks exist in the various universes of the comicbook companies. We know from several issues that characters like Superman and Captain America (Steve Rogers even was the artist on his own comic for a time) have their own comics licensed in-universe, but we're pretty certain that its not openly known that Superman is secretly this one mild-mannered reporter at a great metropolitan newspaper. So, how much is known about the characters personal lives and secret identities?
In a Trek example I wonder if Odo would have taken an immediate dislike to Admiral Jarok given his "vague" resemblance to Dr. Mora Pol.
What about Worf not looking more closely at "K'mtar" given his similar looks to Jarok...