With the breakout board and a connected battery there is power on the RTC backup battery input. Regarding the sleep/power states I believe a click on the button has no effect with the latest release. Yes sleeping with 17mw and wakeup configured by an alarm timer would be great. Even a complete boot-up via alarm allows for periodic processing.
We need to look into the kernel source to investigate about the button behaviour, I still have not found how to get the kernel source or in which package it is saved. I downloaded the Linux kernel source "linux-3.17.4" from kernel.org but it seems that the Edison support is not in there.