Does restricting background data for an app turn off notifications too? Does restricting background data also stop my phone from receiving notifications from restricted apps?

For example: I go to Settings > Data usage > Cellular data usage > Facebook, then I turn off 'Background data'.

Will I still receive notifications from Facebook?

Note* I am on Android: 7.1.2 and Device: Pixel

Thank you,

Dan
If you're still connected to WIFI you should still receive those notifications. It sounds like you're just turning off the mobile data(as stated on my Galaxy S5), but not the WIFI data. 

If you're not connected to WIFI you shouldn't receive notifications because it takes data to check for updates with the Facebook app.