It does, yes.. but we had a bunch of days in the thirties* where taking the Mojo out of its case and balancing it precariously didn't cut it. That said, I really shouldn't have to balance a device on its edge to stop it from switching itself off- that's rather poor. Hell, it shouldn't be a necessary to take it out of its protective case, either, and cross your fingers that running it from the mains won't make it shut off.
It was a blessed relief to get the Modi Multibit, as I was always on edge when listening, expecting the music to cut out, when using the Mojo as my desktop DAC.
Between the thermal issues when charging, and the advice to put your phone in flight mode while using it (due to lack of RFI protection from the USB), it's a good job that it's a niche audio nerd product. We're used to things like the Mojo and the GeekOut series which sound fantastic but have annoying usability problems- we prize the sound quality over convenience. If it was a mass-market product, the consumer advocacy organisations would go nuts and the memes would also proliferate.
Luckily the sound quality is decent and it drives my smaller headphones (especially IEMs) nicely, otherwise I would have returned it as faulty already!
*Celsius, obvs.