I am familiar with YUMI, and I don’t see any reason why it wouldn’t work on a Pi. I’ve booted into NOOBS, which is the shipped OS for most Pis, on an SD and done a live boot to Ubuntu on a USB drive without a single issue. The problem with the Pi is that there’s not a ton of local RAM to use, so you’re forced to local cache on the removable media. It doesn’t slow anything down, it’s just a consideration if paging is an issue in your OS.
Food for thought...
I think that the 1GB RAM on the Pi2 will be very sufficient, so long as the YUMI bootloader is recognized by the BIOS on the Pi. Puppy Linux requires very little RAM to begin with and you make it sound as if more demanding distros run just fine.
I’ll be getting a couple of these soon to play with, just as soon as I find out what to do for a display, as I have no HDMI monitors or TVs at this time.