This is a horrible phrased question, there are so many factors to consider.
First, most free-market proponent, and even most anarcho-capitalist will agree that there is a necessary function of the government in a capitalist economy. Even in a truly free market, there needs to be a general guideline for conduct (contract law notably), as well as a place to settle disputes in relation to those guidelines (judicial system), as well as a mixed bag of other albeit less "economic" functions (defense, etc).
Now, despite your definition, as we've seen through our current economy, the whole idea of capitalism is a slightly ambiguous term. You really need to look at the entire economy to question whether government is necessary. Are you going to have a purely barter economy? If not, what kind of banking system would the economy have? If there was fractional reserve banking, would those banks be supported by a centralized reserve bank? What would be used as a medium of exchange? Gold? Gold backed currency? Fiat currency? If fiat currency, who would regulate and control it? I mean, if we're talking about the US dollar, you really have to think about the implications there as well. Since 1971, the US dollar has essentially been akin to gold in that is a universally accepted store of wealth - which has further implications when you start to think about the fact that the US government could essentially print gold (not really, but you get my point). That isn't even considering aspects of monetary policy conducted by a central governing body, which is something I won't get into...
So to answer your question, no. A free market economy certainly can exist in a variety of forms, but unless we return to a barter economy (and even then not really) we need some sort of governing body (not necessarily a federal government) to provide those fundamental and very limited guidelines and services.
I happen to be a proponent of the Austrian and Chicago schools of economics (there are aspects of both I really like; and yes, I know they're not the same thing..) which both tend to favor free markets. However, despite what the MSM and people like Krugman would have you believe, even us wacky free-marketers understand the need for limited regulation. The disagreement has never been over "government" or "no government" - it has been about "how much government". History has shown time and time again that intervention in the markets leads to unnaturally large bubbles that eventually burst. This all stems for the Keynesian idea that we can promote constant economic growth through the use of monetary policy to avoid down turns in the economy. There is a lot of debate about this even among economist, but the thinking I tend to agree with is that intervention through monetary policy only exaggerates the natural highs and lows of the business cycle, something which I tend to think is undesirable.
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