Absolutely, yes it is possible to test positive for antibodies and then negative for the virus itself. This is what happens when you clear the virus naturally or through drug treatment (as I did). Statistics vary on just how likely any one person is to naturally clear hepatitis C on their own (i.e. without treatment). The common statistic that used to be used is about 1 in 5 manage to clear HCV on their own during the acute (early) phase of infection without the assistance of drugs. But in recent years I've seen that statistic change from many sources in a manner that suggests that more than 1 in 5 clear naturally. Like maybe 1 in 4 or even 1 in 3, depending on the circumstances. It seems current thinking is that natural clearance of HCV is more common than once thought, especially amongst certain groups of people.
For instance when I was infected with HCVback in the 80's, I was in a really bad accident that caused mass trauma. My body was severely injured and weakened, and just at that moment of severe injury/vulnerability I was given a whole pint of infected blood, thereby transfusing me with a *massive* instant infection of HCV which consisted of billions of HCV virons suddenly entering my body. And just at that precise point in time when the blood was transfused, my body was struggling to survive and recuperate from the immediate life threatening trauma sustained during the accident and surgery. So I'm quite certain my immune system functions were less than optimal at that time, plus I didn't eat a thing for nearly 2 weeks afterwards. So under circumstances like this, the stage was set for an almost certain chronic infection of HCV. The virus entered the body in a huge quantity just a time when its defenses were down, thereby almost ensuring a permanent foothold within the body.
On the other hand, other exposures are much less likely for the virus to establish a successful chronic infection. For instance, someone who is in good to excellent health with a normally functioning immune system and somehow is exposed to only a tiny amount of HCV infected blood almost certainly has much better odds of clearing the virus naturally when compared to the scenario described above. A tiny exposure to the virus means it takes the virus time to replicate and build up to levels where it is more likely to have a chance of becoming established within the body. And that time lag is what your body needs in order to help identify the virus and mount a strong defense against it before it gets a good foothold within the liver and elsewhere in the body. I also think that those with allergies or otherwise somewhat overly sensitive/hyperactive immune systems are probably more likely to clear the virus naturally. I don't have proof of that, it's only an opinion, but I do think that those with allergies have immune systems that are more "on guard" than those without allergies, and this may serve to protect them from foreign invaders in certain circumstances (perhaps like those associated with a HCV exposure).
So as you can see not all exposures and not all people who are exposed are the same. The statistics that have been used over the years to describe the likelihood of becoming chronically infected are pretty fluid from what I have seen. The reality of the situation is that the real likelihood of chronic infection is individualized based on the person, the exposure modality and probably to some extent the virus itself. But in my opinion, I think if you are a healthy person with a healthy immune system and your exposure was a very small one (in volume), then I believe your odds of clearing the virus naturally are better than 1 in 5. How much better is not possible to say, but anecdotally I've seen people clear naturally during the acute phase several times on various internet forums in the past and with someone in person as well. It definitely isn't some kind of extremely rare or highly unlikely occurrence. Just take a look at ajw543’s current post here on the forum as just one example:
http://www.medhelp.org/posts/show/510751