Here comes my 2p.
I have owned several types of pit, kettle BBQ's and I own a single gas BBQ. I have cooked on all without wood with the exception of the pellet smoker that I used to own.
When cooking indirect, there is rarely a time when I have a need to cook without wood. I have an oven that is perfectly capable of holding a low temperature, I also have a stand alone slow cooker. If I want to slow cook without smoke, I just use these tools.
If I need extra capacity, I have the option of using a pit as an outdoor oven without wood. It does affect the flavour but only subtly.
To be honest I don't care too much what people call "proper" BBQ. Opinions vary wildly and I respect those opinions as long as people can justify them and don't just spin out a load of BS claiming to be BBQ experts/evangelists.
Now when it comes to competitive BBQ we're talking a whole different animal. There are clearly two paths. Firstly there is the gourmet grilling such as Ready Steady Q and Laverstoke where you are talking about a cooking competition using BBQ's. These are open in terms of style, use of smoke, flavour profiles etc.
When you consider Low 'n' Slow style competitions, these are an American concept so guess what, they are based on the American definition of BBQ. This being the slow cooked, smoky meat feasts we all know and love. There are expectations involved in judging this type of food, the meat will be soft and succulent, it will have certain flavour notes, one of which being smoke. This would be the expectation in an American competition where BBQ is considered as food cooked over wood.
But just a note for you, MiM 2011 a team placed with jerk chicken that had no discernable taste of smoke. Pit Masters round 1 2010 We won chicken with an entry that had no smoke on it (we forgot

).