Yes, the light will "spread out" past the focal point. I don't know that it would make it "worthless" for signalling if that's all you had available, but a plain flat signalling mirror will be better, lighter, smaller, easier to aim, and cheaper. Plus parabolic mirrors are "front surface" mirrors. Which means the reflective coating is on the front of the glass, not on the back side of the glass like a normal mirror. Front surface gives you better reflectivity and better imaging, but it is terribly prone to scratching and deterioration of the reflective coating. You don't want to go touching it with your fingers. You have to really protect it. For telescopes you want a front surface mirror because if the reflective coating is on the back of the glass like a normal mirror, you will also have a faint reflection coming from the front of the glass (just from the glass itself, not because of any coating). This double reflection is not what you want in a telescope, but it's fine if you're just shaving, combing your hair, or signalling airplanes.

Bottom line - unless you're building a telescope, forget about a parabolic front surface mirror. It's not what you want for emergency signalling or firestarting. Cool idea - but just not practical.