Investing with your emergency fund is not a total bad idea at all because after you have might paid all your bills and the money remaining becomes your discretionary income and inside that your discretionary income you can still generate out your emergency fund and started investing in the last 6 months and think you to invest using your emergency fund so that it multiple more income since you are not using it at the main time, you can invest with the emergency fund and tage it emergency fund which means it can be pull out if incase of unforeseen circumstances that might happen, so the reason why we should invest emergency fund is to back your really investment incase of anything, so you can decide on what to do with your emergency fund as per dividual convenient or best know to you, if actually you needed your emergency to in cash but left with me, i will say that once you progress with your Bitcoin portfolio that there are always a need to invest to have emergency fund.
While am struggling to really understand your point the fact is that it is wrong to invest with your emergency funds and there is no smartness in doing this at all it is called an emergency funds for a reason which means it has to be ready for the real reason of it's purpose, you sound as if you know when emergency will happen, nobody knows when this will happen and the level to which it will happen investing it is risky and it is not a good thing to do and is a total bad idea and advice if you ask me.
When someone has very little knowledge about risk management, someone talks about investing with an emergency fund. From my point of view, there should be such a risk management where the emergency fund will not be needed even in an emergency, that is certainly in the initial stage of an emergency. Investment is not urgent in any way, so planning to invest with an emergency fund is undoubtedly foolish. Protecting the investment fund is more important than increasing the investment fund. If you are about to sell the fund while increasing your investment fund, then it will definitely not make sense.
So you should have such a risk management in which you can struggle with the emergency for about 1 year. For this, you should have sufficient cash flow and reserve fund in your backup fund which will help you struggle for 7-8 months. Then if the emergency is not resolved even in this long time, you can take help of the emergency fund. Although the main function of cash flow and reserve fund is not to resolve the emergency, there is no problem in doing so if necessary. However, you cannot use the emergency fund for any other purpose, this is wrong.