Doubtful.
If people are really serious about this, then they need to construct a real petition actually signed by people in the individual politician's constituency. And then mail the hard copy to his or her office. That's how things are done.
An online petition where anyone can put any false name/address and will contain addresses outside a specific politician's constituency is easy to ignore.
If you were a politician, and you received an e-mail like this with supposedly accurate signatures from people who don't vote for you, would you really take it seriously?
It will get deleted by some staffer before it even gets to the politician's inbox.
Hardcopy delivered by the mail with voter's names on it is the way to get the attention of a politician. Sure it is easier to go to some website, but it is that ease that decreases the petition's effect.
If a politician can see that people who can vote for him/her are willing to expend the effort to make a real petition, pass it around, verify names/addresses and present it in a serious way to the politician, that will get their attention.
Sometimes the old ways are still the most effective.
But they take effort. The real test is how committed are the people supporting this effort? Just committed enough to visit a website? Or committed enough to make the effort to formally redress their grievances to their representative?