It's not important to create an emergency funds before starting your Bitcoin investment, because it's irrelevant. No need to keeping too much fiat on you when you don't have any bitcoin. Emergencies may/maynot come, but it's good to prepare for it. This is why emergency funds shouldn't be our priority but buying bitcoin should be, because bitcoin price waits for no man. You are investing on a long term investment and you have all the time to build your emergency funds as you are investing. Your emergency funds is a backup to your bitcoin investment and not your bitcoin investment been a backup to your emergency funds. There must be a bitcoin investment before your emergency funds will be effective.
It's only viable if you don't have almost any cash intact and would
have to oblige and get out of the market by, unfortunately, selling off your BTC.
Other than that, BTC investment doesn't have any risk to it at all.
Situation will depends on financial capabilities but I guess its basic that we don't need to set up first our emergency funds when starting up since what actually needed to pay attention first is to execute our first accumulation. We could just set it up later on especially once we already established our portfolio since everything will be done if we already set some goals and include that in our plans.
Also we don't need to sell anything just to set it up since we could just spend some extra cash for this usage. I also don't agree with what you have said that Bitcoin investment doesn't have any risk attached since you also need to consider the market volatility and other market disturbance like fuds spreading. So don't expect any unrealistic with Bitcoin so that you will not caught up on some wrong thinking that might cause damage on your investment.