A separate google account isn't going to matter
If you ever login to ... well, about anything given all the Google ads from doubleclick etc. everywhere ... from work, that's enough for Google to be able to link your work PC to your home PC. If you ever login to Facebook from work, that's enough for Facebook to link the two.
All having a separate Google account will do is allow Google to know both are owned by the same person. And I agree with others, why the hell do you login to Google at all??? You might as well send them naked pictures of yourself, that's probably the only thing they have left to collect on you...