I've played in a D20 modern campaign where we went from 1st to 19th over the course of 8 months of playing (2 to 4 times a week). There were a total of 5 combat scenes the entire campaign.
It is still the campaign I compare, and fail to live up to.
Yes and it can be fun. It really depends on the players and what they are doing. Conflict is great for creating drama, and the storyline CAN get stale with combat now and then. That being said, yes we have gone entire sessions without combat and they were fun.