How to (try to) suspend and how to tell if it was suspended?

[Alho]

In addition, hibernation means the CPU is completely turned off, so it will likely not respond to wakeup requests from the modem, i.e., no incoming phone calls for you.

In Hibernation the phone is completely powered off - which includes the modem. As such, this state is useless for a phone. The only way to wake it up is the user pressing the power button.
Hibernation is only usefull for starting the device up faster than a normal boot; but as Kevin said, this has a had impact on the storage (SD/emmc) so should be avoided on a phone.