Considering bitcoin investment as emergency money doesn't seem a bright idea because this will mean that once you need the money you should sell it a market value and sometimes it could be below your entry point.
The exit strategy is a long time movement because you must wait for the right price to convert your money into fiat so you won't be able to have access to your funds right away.
Emergency money should be in fiat.
Yes, you are absolutely correct! When we say emergency money, it means when you need the money you can have it right away. But what happen when the time you needed that money and the price is so low? Probably you will not gain a profit. So, I think it is not a good idea to have bitcoin as emergency money, rather it is so good for investment.