Does Restricting Background Data of Google cause Battery to drain fast ?

[TheAndroidPerson]

This might sound silly. But theoretically speaking, does restricting background data of Google App and Google Services cause the battery to drain faster than usual just because they try to connect to the internet every now and then ?

I observed that when I am on WiFi, I don't see Google Services topping my battery usage list as it does when I am running on Mobile Data (I do have my Google App data background restricted)