Barrel = Colorado River @ Dotsero - 1300 cfs or so.
Barrel Springs is running right now. The flow in Barrel is generally about 1200-1300 cfs less than what the gauge for Colorado River @ Dotsero is reading. This is due to to diversion tunnels/penstocks that divert water from upstream of the dam at Hanging Lake exit to the Shoshone power plant where it is put back in the river. I believe that the max capacity for running the turbines is somewhere around 1300 cfs. Occasionally, Barrel will have water in it when the flow at Dotsero is less than 1300, and the power plant is shut down and/or the "gates" at the dam are open during maintenance. Also, sometimes at higher levels, the power plant is not operating, and all the flow runs through the river bed. But if the plant is running and there is more than 1300 cfs in the river, the difference flows through Barrel Springs (and Upper Death/Life After Death). There is no gauge on the river between Dotsero (Colorado River below the Eagle confluence) and West Glenwood (below the Roaring Fork confluence) that can measure the exact flow in the Barrel Springs section.
So, to make a long story short, I would say you need about 700 cfs in the river bed at Barrel Springs to make the run worthwhile. Therefore, if Colorado River at Dotsero is 2000 cfs or higher, Barrel is good to go without a visual.