Will using gum as mulch grow more gum ball trees?

I have these huge trees in my yard that shed gum. (Not sure the sceintific name for them.) I was thinking its so many I should do something with them. I don't want to start a compost thing if I don't have to. Can't I just section off my flower beds and throw them in their on top of the soil? And if I do, will it sprout gumball trees? I don't want more, I have a gagillion spiky as it is.