Hmm. I downloaded a free book from Kobo, opened it in ADE successfully, then attempted to side-load it to the Kobo reader iPhone app (which explicitly supports File Sharing in iTunes). It refused to open it ('no NCX'). I also used iTunes File Sharing to add it to BFR's documents. BFR opens it!
I downloaded the same title directly to Kobo4iPhone and it opened. But it seems to insert extra, blank pages (at least in the first few I sampled). I've had it crash as well. And iTunes File Sharing seems not to work correctly (does not show me the books Kobo reader actually has on my iPod), though I was able to side-load a non-DRM ePub to it. Another reason to use BFR instead...
There doesn't seem to be any way to side-load ePub files of any kind to the Nook apps (PC, iPhone). They don't recognize anything without B&N flavor DRM. I don't have a Nook device, but presumably (?) it doesn't have this issue, and is back-compatible with previous Adobe DRM.