You should never buy BTC with emergency funds. Many people see the market fall and aggressively use the emergency funds they have at that time, which is completely wrong. Emergency funds are created to deal with unexpected financial disasters. If you invest with your emergency fund at that time, if an unexpected financial disaster comes, then you have no choice but to sell your holdings. In some cases, you can invest with emergency funds.
You are absolutely right investing in Bitcoin with ones emergency funds is already a wrong investment and it is more like a waste of time because the person is going to sell the investment definitely and it can either be in loss or in profit depending on when the need arises so investing with emergency funds is as good as not investing at all because there is no need since you will sell off when situation comes up. A wise investor or a learned investor will never think of doing such because they know what is at stake.
For example, you have the money to buy aggressively, but you may not be able to invest with it due to some problems. For example, you are not able to transact due to some problems or errors in the bank where you have deposited the money. You know that after some time or within 2 or 3 days, your bank account will be fixed or you will be able to transact again. But you have to be confirmed that you will get the money after some time. In that case, you can invest for some time with emergency funds.
Your example is quite alright but I want you to know one thing and that thing is that in life nothing is certain, talk of more of bankers that are humans and they can be so funny and dramatic or will I use the word annoying because an issue may seem so simple and easy but bank will frustrate you I'm saying this out of experience I have had a little problem with my bank and it was a problem I think can be fix or rectify in an hour but they frustrated me, sometimes they will ask you to get some documents you can not be able get at a given point in time so what I'm saying in essence is that you don't risk what you just said because bank is not sure even if they promise you, there are somethings you should not do regardless, if you don't have at any point in time forget about it I mean it is not the end, you should not allow a minute or an hour mistake to ruin your years of holding that will be crazy.