Absolutely not. I use Gmail as my primary email address, and my start page in Firefox is also Google.com, but Desktop, Toolbar, etc. aren't allowed anywhere
near my PC. I did say I'm a young tech, but that's Troubleshooting 101, Doc.
To confuse me further, though, this problem seems to come and go as it pleases, which makes it harder to troubleshoot, since I can't always replicate it.