Connection to Google vs not

Hi there.

Curious question.

I have 2 wifi networks at work (a library) and our public one is wide open and connects to google fine - green bars over wifi on UD 3. If i use our private one, they stay white due to ports being blocked and i noticed more battery drain.

Think that no connection to google would cause a drain? i thought so becasue it would keep trying to connect.

PZ