No, they are not, at least in the specific case of 2011 White House system.
If you look at the responses to that White House site, any of the important ones are basically articulating existing policy positions of White House/Obama administration.
On petitions that are being responded to, if the petition contradicts WH position, the reponse is a canned restatement of what Administration party line is, frequently not even tailored to actually respond to petition.
In other words, such a site is a way for politicians in power to allow the people to feel important and vent, as opposed to being a tool to take a pulse of the nation and respond to popular wishes (or, at worst, to achieve its political goals - see below).
If you petition for something important that the government wants to do, they would do it even without that petition.
If you petition for something that they disagree with, they won't change their stance (and given the current US political climate, why should they when 50% of population holds views opposite to the other 50%?).
As the most glaring example, they outright rejected building a Death Star :(
This is being corroborated by a "Time" magazine post, discussing the origin of the system and the reasons WH likes it. While it has no good sources cited, Time is very pro-Obama in general so I'll tend to trust this somewhat less-than-flattering snippet:
It started as little more than a whiteboard jot in the Eisenhower Executive Office Building, a simple idea to get millions of Americans to contribute to the White House website. Imagine a scenario in which a gun-rights group starts a petition to tell Obama not to confiscate guns. “Wouldn’t it be great if we had the opportunity to respond to all these people directly and say we are not interested in doing that at all?” the White House staff mused. It would be a new digital main line to opponents, a way around organizations like the National Rifle Association.
Notice something? It's not "for Administration to hear the opinions of gun rights groups". It's for them "to be able to RESPOND to gun rights groups". Another communication option for White House Press Secretary.
If one is being even more cynical, such petitions can (and may be even are?) used by political operatives to make a pretense of popular support for the government policies. Since the opponents of a policy have no way to respond to pro-government petition, you basically make a very convincing pretense that a large portion of population agrees with it, without any sign that an equally large portion of population disagrees with it. This was done by "letters to the editor from common people" in former Soviet Union (e.g. the infamous Timashuk letter )