I would have linked to the Bogleheads Wiki MDM linked to.
Remember that an account and an investment is not the same thing. You hold an investment in an account. Accounts can have different tax characteristics, but other than that, they don't have different returns. Given that, if you've decided that one year of expenses is the appropriate amount for you to have in an emergency fund (in the sense of liquid, unlikely to lose value holdings) then considering your Roth to be part of your emergency fund is fine, but that portion of your Roth should not then be invested in equities. Whether or not you need a one year emergency fund is another question, but that's independent of whether part of your emergency fund should be in a Roth account. That's a question of how much you should hold in "cash" (or other stable value investments) and how much should be invested in equities.
All that said, if you can't currently afford to max out all of your available tax advantaged accounts and build/hold the emergency fund to the desired level, then I think considering part of the Roth to be your emergency fund (and investing it in stable value investments) and putting the taxable emergency fund into tax advantaged accounts is a great idea.