John,
Smoke is a rather potent "spice". Like salt or chili powder or curry, there is a fine line between just right and too much. How much you like it depends on several factors:
1. Type of wood (example: fruit vs. hickory)
2. Amount of smoke
3. Quality of smoke
4. Flow of smoke (top vent should be open)
5. Type of meat
6. Thickness of meat
7. Sauce and sides: some compliment smoke better than others
8. Your "mood" at the time
Chicken: Most people say that chicken is very easy to oversmoke.
Ribs: Since they are thin, every bite you take will likely have lots of smoke covered meat. So ribs can also be oversmoked. Compare this to a pulled butt, where the smokey outside meat is mixed (diluted) with the non-smokey inside meat.
Regarding #8: Sometimes Chinese food sounds great to me, other times not so much. It's kinda similar with smoked foods. Granted, its rare anymore that I'm not in the mood for smoked food, but it does happen. Most of the time, my wife catches me at the fridge sniffing the leftover containers the next morning.
Maybe its just me, but sometimes I get desensitized by the smoke after a long cook. The scent is in my hair, on my clothes and skin. For me, a quick shower and change of clothes before dinner can make it taste much better.
Don't give up! To answer your original question, I don't think it's a matter of time to acquire the taste. Rather, it's about finding the magic balance between:
1. Type and amount of smoke
2. Type and size of meat
3. Your personal taste