Are you saying you want to put your emergency savings in the market, or that you have excess money in an emergency fund and want to invest it?
Perhaps both?
Emergency money shouldn't be in the market
Why? Would be easy to double and make the taxable account have more money in it to mitigate risk significantly.
The question is confusing because it's actually a little ambiguous.
If you have no other accessible funds, then the emergency fund shouldn't be invested in the market. The idea of an emergency fund is how much you might need in case of emergency. If that amount is down 20% in the market, you don't have enough for the emergency.
If you have accessible funds sufficient to cover an emergency, then the question is really whether you're okay that you might have to pull e.g., $10,000 from your after-tax account after the market has dropped 20%, thus costing you a couple grand. If you expect only rarely to have an emergency, then I would think that's an acceptable tradeoff to just put it all in the market.
We don't have an emergency fund. I can cover most stuff by charging on the credit card and paying it off by the due date, and as backup, we have a home equity line of credit (never used, but available) and could sell funds from our Vanguard taxable account.