The doc is and always will be property. Otherwise, you could never use a holodeck because all the holo characters would always be "alive"
However there have been instances where holo characters have developed self-awareness if left on too long. This was established back in TNG with the Professor Moriarty character in the Sherlock Holmes program. As for Voyager's emh he became self-aware again from being activated so often. As Janeway told him, "You don't have the luxury of only thinking of yourself as a hologram." Not only did he become a member of the crew but he fell in love, developed his own hobbies and friendships, etc.
The question of his sentience was settled imo during "Latent Image." At first, the crew treated him like a machine and tried reprogramming him when his moral dilemma caused him to "malfunction". Eventually they realized he would just have to suffer through it like the rest of us would in that situation.