Does Enterprise Manager predict failure of a BIG-IP system?

EM can collect stats and alert on certain conditions. check the alert settings/options.

NTP needs to be in sync between all devices and EM device where you want to collect, otherwise it doesn't work...

from "failure" perspective, depends on what you mean. it can alert on certain conditions...

like fail overs happening, software installs failing, but nothing on cpu/mem, etc... ;(

cheers