That’s one way a VPN helps. Assume the FBI knows your IP address (they got it from your ISP). They fax Google for a list of searches conducted from your IP address. Result: empty (because all the searches will show up to Google as coming from the IP address of the VPN service provider endpoint, which could be in another country and which could change from time to time).
That is not the whole story though if you are really a person of interest.
Now about that cute furry sex costume …