Well, a letter writing campaign helped save the original star trek tv show, but as to how effective they are today here is a quote from someone who would know, the man behind Babylon 5 and Jeremiah, JMS:
I would image that an online petition would have even less influence than a letter writing campaign, but I certainly share your sentiments. Firefly is a good show was great potential, I would be terribly upset to see it go. If Firefly is not a success it is fox’s fault; no wonder it is having trouble attracting an audiance with the terrible advertisements they ran for it, and showing the episodes out of order.
I’m signing the petition only because I would, for once, like to see a letter-writing drive save something worthwhile (or at least created with talent) and redeem humanity for the fact that people actually saved Star Trek (in any incarnation) and Quantum Leap, my two most despised series of all time.