Yes.
https://github.com/Fourdee/DietPi/issues/509#issuecomment-246702824
Running DietPi on a USB HDD w/o SD
All Raspberry Pi’s ?!
I will say no.
What’s about Raspberry Pi-Zero, Raspberry Pi Zero W, Raspberry Pi B+ , Raspberry Pi B, Raspberry Pi A, Raspberry Pi 2, …?
I have: https://github.com/Fourdee/DietPi/issues/509#issuecomment-246734927
And, unfortunately seeing no advantage over moving filesystem to USB devices. Only drawback and rising boot up time. Sorry.
But you can do as you like.
https://github.com/Fourdee/DietPi/issues/509#issuecomment-258833304