vic didn't really develop an inerest in economics, doing the books was part of his programmingno, Vic was always aware that he was a hologram, he never had a desire to change anything. The only thing that changed for Vic in that episode was that from that point on Quark said he would keep him running all the timeWeren't some of those questions addressed in "It's Only A Paper Moon?" Vic Fontaine's extended period of operation led him to deepen his understanding of human psychology and a desire to manipulate his environment (at least within the confines of 1960s America).
You asked whether continuous operation of a holgraphic program, one that is programmed to adapt and learn from its circumstances (which both EMH and Fontaine do, albeit to different effect), affects their development. Vic literally says so in the script. Did he need to develop an interest in music? No, but he develops an interest in economics. The fact that he doesn't intend to live outside the confines of simulated Las Vegas isn't material. The episode even raises the question of Vic having free will (though it doesn't answer it). Does the program need to desire to grow in order to be alive, no less sentient? I guess someone who sits at home, watching TV, could be said not to be alive in a figurative sense (which is what Nog does in the episode), but it cannot be said that he or she is not living.
my question is, is the desire to grow a true unique desire, or is it programmed into them, is there a line of code that tells them to desire to grow beyond their initial programming