What would happen in Venezuela if the government all of a sudden starts offering currency exchange by the prices of the free market?
To my knowledge, the main reason for the government in Venezuela to have currency exchange controls is that they don't want everybody to start buying less volatile currency in order to protect their savings from inflation. What would lead in turn to the government losing all of its reserve currency.
Would that hypothesis hold true in such situation?
You could probably think about the policy trilemma. It's the idea that a country can only have up to two of the following: free capital flow, a fixed exchange rate, and independent monetary policy. Right now it seems that Venezuela wants a stable currency exchange (so they control it) and they want reserve currency available to stabilize the economy if need be and have independent monetary policy.
So if you got rid of currency exchange controls so people could buy foreign currency more readily, in the short run, you'd lose control of the exchange rate without gaining anything. Long term, since the money market is clearing, and assuming Walras' Law holds, then capital will be able to flow more freely and contribute to economic growth. It might force Venezuela to be serious about not causing hyperinflation for that to happen that.
