It could go either way, and probably depends on things like which GDS your travel agent uses and when they do the ticketing. I've had this go both ways before.
The first time, I had two different return flights booked from South Africa (despite having fully flex tickets, both were looking very full so I wanted to make sure I could definitely get on the one I wanted) - this was fine when it was just a reservation but the system wouldn't actually let me ticket anything until I cancelled one.
The second time, I had two revenue tickets (in different cabins) booked for the same flight at the same time (not on BA, this was on *A) and neither got cancelled (I was called back early from holiday and the expense policy wasn't clear on which cabin I could claim for). The one I didn't use showed as a no-show and I got a refund later.