If you can't otherwise max out all of your tax advantaged space, then
moving your emergency fund to a Roth IRA is not a bad idea at all. The basic thinking goes that you were going to "lose" that available tax advantaged space anyway, so you may as well put your emergency fund there since best case scenario you never actually need to use your emergency fund, and eventually maybe you will be able to max out your tax advantaged accounts and replenish your taxable emergency fund. In this case you end up with more in your tax advantaged accounts than if you hadn't done it. Worst case scenario you do need your emergency fund, you can always withdraw contributions from Roth, and you're no worse off than if you'd never contributed. In this case you've spent your emergency fund and have the same amount in your tax advantaged accounts as if you hadn't put your emergency fund in your Roth IRA.
That answers the question you asked in the thread title, but you go on to talk about getting a better than 1% return, which is an entirely different question of whether you should invest your emergency fund. You can invest either in or out of an IRA, and you can hold low risk "cash" like assets in or out of an IRA. In fact, in terms of tax efficiency, holding the investments outside the IRA and the cash like (interest bearing) assets inside the ira could even work out better given how interest and capital gains are each taxed. Anyway, you should not invest your emergency fund as that defeats the purpose of an emergency fund. You may at some point decide that you have access to enough assets that you don't need an emergency fund because even in a large market downturn you'll have enough to be ok, but until then don't invest your emergency fund.
If you decide to put your emergency fund in a Roth IRA so you don't lose the tax advantaged space, but not invest it so you still have a viable emergency fund, then you might decide to open an IRA at an online bank where you can keep the assets in a savings account or CD. Ally would be a good option:
https://www.ally.com/bank/ira/ira-account/. Bonds would also be a fine option if you'd rather have your IRA at somewhere like Vanguard.