No, emergency funds is not basically for investment infact that's not their primary purpose, just like the name implies it's used for unplanned financial issues in the future or near future for instance medical bills, auto mobile fixing bills or support for a bill that can't be taken care of by the discretionary funds, those are the duty of the emergency funds whereas funds that's mainly for Bitcoin investment is the discretionary fund.
The emergency fund can only serve as a discretionary funds in a case where an investor lose their job then get support from the emergency funds to be used as discretionary for the time being till the person get another job. @Out of mind, yes you're right the emergency funds would only be used for investment as protective measure when the investor can't generate discretionary funds for the time being.
Using Emergency Fund To be clear, I can say that use emergency fund only when your emergency has reached a stage where you have no other funds to solve it except the emergency fund. That is, you should not reach for emergency fund in the initial stage of any emergency.
You may have cash flow, so use cash flow at the beginning of the emergency. If the cash flow ends, then ask for help from the reserve fund. If the reserve fund also fails, then go to the remaining other funds for help. Still, if your emergency does not go away, then try to solve your emergency from the emergency fund at the last stage. If you take steps during your financial crisis in this way, then maybe you can spend 6-7 months of financial crisis. I hope no one faces financial crisis for such a long time. The expectation is maximum 2-3 months which can be overcome with cash flow and reserve fund.