Cryptocurrency can develop without fiat market, however they're mutually connected to each other. Cryptocurrency still has the less influence on the market of fiat, while fiat market has bigger influence on cryptocurrency. Fiat market has bee nexisting for many years and almost a century, while crypto is too young for being influential. In my opinion, traders always have to pay attention to fiat market when they trade crypto, because the vast majority of accounts are attached to TetherUS which is attached to the US dollar. So, as you can see it's almost impossible to imagine crypto market without fiat, but it might be possible in future.