How so?
If your cell tower is not near you and you have 2-3 bars signal, then that can't be better than reception of your router that is 1-2m away. Of course there is drainage if your wifi constantly goes on and off instead that it is always connected.
Bad reception = slower network = delayed notifications
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That periodically is not push and that's why we have delayed notification. If it stayed connected then notifications will come as a push.
It doesnt matter if the cell tower is near or not, if you're getting signal from your carrier you will get notifications. Its a very small amount of data used anyway even though you think turning off carrier data will save you GB's of data