Setting up emergency fund is supposed to be considered the right way to approach bitcoin investment, even if surely most people may not consider it necessary when getting started. But I still feel that our emergency fund need to come first before any other thing, because getting started with the hope of setting up emergency fund along the line seems very risky as we don't know when emergency issues will poop up.
With adequate and proper funds allocation investment can be built along side with an emergency funds simultaneously, what is needed is to ensure that there is a discretionary income available to start your investment with a sound mentality of also allocating a certain portion for your emergency funds, you don't necessarily have to build up an emergency funds before starting your investment, work on your cash flow management skills and funds allocation, I don't see any risk in building your investment alongside with your emergency funds.