Yes the Roth has to sit there for 5 years, and yes you cannot make catchup repayments into the Roth if you need to pull something out.
The question becomes Risk and Risk tolerance. I don't think anyone should start a Roth as an efund and not have a back up in those first five years. However, if you have your finances stable, your costs low and like MMM proposes have some flexibility so that if SHTF you could tighten down your costs + pick up some extra work in a month where an emergency happened I think using a Roth this way is a viable option.
To me this means debt payed off (maybe mortgage left), a sinking fund for irregularly irregular costs, and the ability to pay for regularly irregular costs already worked into your yearly plan. I guess I think this works mostly for people in MMM like retirement or close to being there.
How often outside of irregularly irregular costs (water heaters have a life of 10-12 years, cars will probably need to be replaced around 200,000 mi) does an emergency happen??? Sure we all know someone who has had something happen, but I bet we also know a lot of people who haven't had anything happen. So what are the actual risks and where is your risk tolerance? Any money you use for efunds that you actually pull out and use is losing you future return.
I think CD ladders are another great option, especially when CD rates are decent (at least keeping up with inflation).
Disclosure: I'm not using my Roth as an efund yet because I'm not in a finically stable position. We'll be working on a liquid (savings account at Ally) 3 month fund and then move towards either a CD ladder, or save for a down payment because we want to own a home and that will allow us to utilize springy debt.