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.
That is the problem when you put all your money into investment and never save for emergency because of wanting huge profit which will lose more profit when it downs but you need to sell immediately. Price is unstable which you cannot depend on in every uncertain situation. Better to save fiat for that and diversify it from your investment.