Newsflash! Suckers don't suck!
You know that old gardening tip for tomatoes: pinch off those suckers - they sap energy from the plant? I've even read in a book about growing tomatoes that they will NEVER produce fruit so you should get rid of them immediately. Well, I tested it out myself way back then and that was not true - they did flower and produce fruit. It just goes to show that sometimes even the most repeated garden advice can be dead wrong.
The one time I do pinch off "suckers" and even blossoms that are starting to form on my tomatoes is around the end of the season when I can see that any new tomatoes that form won't even get to a state when they can be ripened inside. My theory is that the plant can then put its energy into the remaining fruit rather than trying to make even more. I haven't put this theory to the test yet though. Perhaps this season I will. Stay tuned!
Some good info and a video about "suckers" and what they are all about is here: https://www.motherearthnews.com/organic-gardening/vegetables/growing-tomatoes/prune-tomato-plants-zmvz15jjzsor.aspx