Yeah, you don't want it doing that. It might not cause problems, but if nothing else eventually it will affect play.
My suggestion, get a tool like this:
http://www.pinballlife.com/index.php?p=product&id=1518&parent=96
It will make adjusting your slingshots (and all leaf switches) WAY easier. Then, I would suggest bending one of them back so it isn't sensitive at all -- I usually do this to the bottom one first, and then adjust your top one to be just how you want it to be (including testing it with the game on). I like VERY sensitive slings, creates more side drains.
Anyway, once that first one is done, do the second leaf switch to try to match the sensitivity of the first one. I will generally put a piece of paper in the second one so that it won't be going off at the same time. Then, test it again.
If they both are sensitive on their own, but aren't machine gunning or double shooting, you should have no issues taking the little piece of paper out of the first one and playing it like that.
No matter what though, you need a real tool to do it right -- otherwise, you bend the leaf switches in the wrong spot, which can cause inadvertent touching and firing throughout the game. Gotta keep those leaf switches right!!