You've got it reversed. Mining activity will be tied to the exchange rate. Total mining rewards (denominated in BTC) are constant no matter how many miners there are, so the higher the exchange rate, the more people mine as it becomes profitable for them to do so. Mining is a zero sum game.

In addition to what tlrobinson said, you only need a small threshold of hash power for a cryptocurrency to function. More hash power reduces susceptibility to 51% attacks for those coins that are at risk for it (including Bitcoin), but it does not impact the functionality of the coin in any practical way.