I was taught the same thing, to break off the sucker branch while it is small.

There may be some truth to what you said about propagating the sucker branch after it is bigger. But, what about the nutrients it is stealing from the main plant while you let it grow? Here is my story about why I think you can propagate a new tomatoe plant from a branch:

Last year, I was leaving the nursury after purchasing a new tomatoe plant. We had strong winds that day and I heard a snap from the plant. I was concerned I had broken my tomatoe plant at the base, but when I looked I could not see a break. The nursury owner said to make sure that I heaped plenty of dirty around the base when planting it and it would "heal." That makes me think they will root in dirt for propagation.