Edit: Sorry, I think I misunderstood your question. If you don’t have Google Play Services enabled but your friend does and messages you, no, a push notification won’t be sent, but if you message them, one will be sent to them.

I thought you were asking if you just disabled notifications on your phone if that would prevent push notifications from being sent. I’ll leave my original answer in case someone else has that question.

It depends on what exactly you mean, but usually not. If you mean in your phone’s notifications management settings, that does not affect the push notifications being sent to Google/Apple servers, that’s just a local setting to decide how your phone handles it.

Some apps, though rarely, allow you to disable push notifications from being sent. If it exists, this is inside a settings screen in the app itself or on the app provider’s website somewhere. Generally, only privacy-conscious apps provide such settings.