Absolutely not. And welcome to the forum. ;)
Emergency funds are supposed to be money that is there for things like a unexpected car repair, medical bill, travel to a funeral... you really need the money to be instantly accessible (or within a day or two). That means a savings account. There are some out there that have ~1% interest rate.
You do not invest funds you might need in a hurry. So emergency funds, savings for a home purchase, or any money that you might need access to within a 5 year or less time period goes into either a savings account or (for the mortgage situation) possibly CDs if you can find some that offer a better interest rate.
The reason is that while the market does always go up, it isn't a straight line, and you can't know if it will have retained the principal value of the investment exactly when you need that full amount.
Say you invest your $5,000 emergency fund. 6 months later, your A/C unit goes out and the repair is going to cost you exactly $5k. Problem is, the market is in a down phase, and that original $5K you put in has dropped down to $3K. So you unfortunately have to sell it all (at a loss), and still need to come up with an extra $2K. That emergency fund just compounded the emergency.
And I have no idea what your situation is, but if you can only manage to save half a month expenses in one year, you really, really need to take a very hard look at your debt/spending habits. Suggest you check out
how to write up a case study and get some triage going.