The inverse is what you're trying to prevent. Service ABC has malicious activity and calls Google to ask which accounts are accessing from that IP address. However this has two main problems.
a) Why would Google give this info over willingly.
b) Most VPN's assign the same outbound IP address to multiple users. So it's not a 1-1 mapping.
c) People who are using a VPN for something malicious are not also signed into Google.. I'd think.
b) You can reduce the list of suspects significantly by correlating activity on multiple services from the same IP address around the same time.
c) You'd be wrong... especially since Google never really forgets who you are, even when you are not signed in.
b) Depends on the country you are in. You might be the only one connected to a specific VPN server at specified time, this also answers point c.
c) Would be surprised. Have a read of this recent Affidavit https://s3.documentcloud.org/documents/23723268/pompourin-af...
Also, you don't have to be logged into google for google to know who you are. If you're using windows, your OS is also phoning home constantly with identifying data. If you use steam, it's also phoning home. Run wireshark sometime and see how much your computer is sending to random servers without you doing anything or being "logged in".
You can counter that easily. That's why you should use a multihop VPN.