The RTA recently published their travel time survey results for 2011. With only a small minority of roads operating with average speeds of less than 20km/h you would be hard pressed to beat the average speed you could achieve in a car. Only Cleveland Street, parts of Parramatta Road, O'Riordan Street, Old South Head Road and Oxford Street are average travel speeds less than 20km/h. Considering that this includes stops you may be hard-pressed to beating the traffic on a bike.
South East Queensland's 2009 Travel Time Survey shows much the same picture with around 65% of the major arterial roads in Brisbane travelling with average speeds greater than 25km/h. With the Gold Coast and Sunshine Coast having 90% and 97% of average speeds on arterials greater than 25% there is even less likelihood of beating cars on longer journeys.
short news report on a race they did between a cyclist and car from east Brisbane to King George Square. On the 5km race the bicycles beat the car by a mere 2 minutes during the morning peak hour. Not much of a time advantage but at least the cyclists burned some fat during the commute and didn't have to pay for parking or fuel. As the cyclists said, they could also be certain that their travel time would be reliable, something impossible for the cars to predict.
So will congestion be forcing people to start cycling? Probably not unless it gets far worse than it currently is and there is scant chance of that happening as it will have serious economic consequences for Brisbane. The best way to get people to choose active transport is therefore to make it attractive (safe and pleasant), convenient (lockers, showers and parking) and make car travel more expensive (charge for long term parking).