Scientifically speaking...
cell regeneration wouldn't be able to destroy the Shanti virus.Our body naturally fights the viruses we come in contact with on a day to day basis. I mean those such as the cold virus and even the HIV virus. The reason why the body does this, is in our immune system are two kinds of cells: T cells and B cells. T cells are the "killer cells" that actually cause apoptosis (cell death) when they come across a cell they recognize as infected with a virus. They recognize virally infected cells, because cells present little pieces of degraded protein on their outer surfaces. In an infected cell, some of the protein presented is
virus protien. In our blood are pieces of protein called antibodies. One side of them attaches onto the presented pieces of viral protein. The other end attaches into a variety of cells (including T cells) which kill the infected cell. So, a "killer cell"l knows what cell to kill, because it attaches onto these antibodies which are in turn attached to the bits of viral protein in infected cells. Without the antibody attaching to the infected cell, the killer cell wouldn't know what cells are infected, and therefore it wouldn't be able to kill them (and destroy the infecting virus).
Every single virus has a different kind of antibody that's specific for that one virus. Each one of these antibodies has a part of its protein that binds to part of the presented viral protein. An antibody against virus A wouldn't be able to recognize protein parts of virus B, so it would never bind to a cell infected with virus B. Consequently the killer cells would never know the cell was infected, and would never kill it, and the cell would continue to produce the virus. Only if the person's blood had an antibody against virus B in it, could the killer cells tell that a cell was infected with virus B. So if the person doesn't have Antibody B, cells infected with virus B won't get targeted by the immune system.
The human body has a
lot of different B cells, each of which produce a different antibody, each of which in turn target a different kind of viral protein. Between all of them we're pretty well protected against most viruses. Some, though, we aren't. That is why we get vaccinated: a small amount of the virus is introduced to our system, not enough to harm us, just enough to activate the B cells which produce antibodies against it. Then, if a stronger version of that virus infects us, we already have a bunch of antibodies against it stored up, and our immune system can destroy it quickly.
So what does this have to do with Heroes?The Shanti virus is just like any other virus. The immune system will only respond to destroy it if it knows that a cell has been infected with it. In order for the cell to be recognized as infected, an antibody has to bind to it, so the killer cell can destroy it. Right now, Mohinder is the only character we know of who actually has antibodies against the Shanti virus. Therefore only an infusion of
his blood will give someone the antibodies they need, so that their immune system knows what cells are infected by the virus and can destroy the infected cells.
Where does that leave Claire, Adam, and any other regenerators?Since neither Claire nor Adam have the antibody against the Shanti virus, their immune system would be unable to destroy any infected cells. That is, their blood itself is not a cure for the virus.
However any cell that the virus destroys, their body will just regenerate. So the virus wouldn't be able to kill them (they would just regenerate the destroyed cells). Now, we know that the virus takes away abilities when it infects cells. So, once enough cells are infected with the virus, those cells won't be able to regenerate. The upshot is, it would take them a lot longer to die from the virus, but it would happen eventually.
All of this assumes that Heroes!science is the same as Real!science in every respect except one: that some people have four genes which allow them to do extraordinary things.
That's why I think the virus should still be able to affect Adam. His ability is cellular regeneration, not immunity to all harm, even though
most of the time they amount to the same thing. The Shanti virus is not one of those "most of the time" situations.
[Disclaimer for other folks familiar with this: I did simplify a lot of the complicated mechanisms to help get the point across. Forgive me

]