Default Keep Awake off and push notifications

Turning "keep awake" off in AppOps prevent push notifications? I want to turn it off on the Facebook app but I still want push notifications.

[DEVICE : N⁴]❌[ROM : crDROID]❌[KERNEL : AK]
[LAUNCHER : NOVA]❌[CARRIER : T-MOBILE]❌[CASE : NONE]