Not till you do some activity. Say if you logged into gmail using one vpn and then swithed to other but your gmail window is idle then the new switched vpn's ip wont be logged. Google will have your ip which you used to log in at first.
I did not get what you mean by "the last time, i had login with password when switched and did activity "does it really work ? the last time, i had login with password when switched and did activity.
Like if I log in with a vpn and then switch to a different server in the same log-in, do they track that?
The easier way to put it is: "Does Google track... Yes."
Clicking something or not isn't going to make much difference these days. Say you got Gmail open, you're on one IP, you then get another IP. Google will know this as the page auto-refreshes to check for new messages. Google Docs will auto save, etc. Just because you didn't click anything doesn't mean data wasn't exchanged.
When it doubt, Google knows.