Whether you invest or not, you need to have an emergency fund
It is never right to invest with emergency funds. If you get sick and do not have money to invest, then you can stop investing for a few days, but it is not right to invest with emergency funds. Emergency funds are not always right to take money, when you do not have any money other than emergency funds, you can use emergency funds if you want.
The emergency funds should not be used for your bitcoin investment or accumulations, your emergency funds which should be able to cover at least 3 to 6 months of your financial expenses should be able to take care of your
medical bills, payment of your utility bills and other financial obligations and not to be used for your bitcoin accumulation.
These are not emergencies but part of your expenses which you should've considered and removed them from the total income before considering the remnants your discretionary income, I might consider the first one "Medical expenses" as an emergency if there is a big medical challenge and not routine checkups or common illnesses that are non-concurrent, but are not emergencies.
The coverage of your emergency funds is subject to a real emergency occurring like car accident, fire accidents in the home and you need to replace some properties ASAP and other things that are that aren't expected to happen. Another scenarios is in the event you are cut off from your income all of a sudden without prior notice and you have exhausted all your savings, then your survival becomes an emergency and you can survive on your emergency fund for the time being while you work on fixing your finances and rebuilding the funds you depleted while you were financially backward.