Thanks for the replies, everyone. I think this year I might at least let one grow a large sucker and try planting it.
mom, that was probably a sucker you heard snapping because I was reading that when they get to that size, they'll snap off cleanly. If there's lots of messy rough edges with fibers, it wasn't a sucker apparently.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.
I'm always up for experimenting in the garden - thanks again for the input!