That's the idea behind VTzilla, a Firefox add-on that scans files for viruses before you download them. Once installed, it adds a Scan with VirusTotal option to Firefox's download dialog box (which appears when you click a file).
VTzilla also adds a scanning option to Firefox's context menu. Thus, you can right-click any suspicious-looking link and choose Scan with VirusTotal. That's great for ferreting out suspected phishing sites (like the LinkedIn ones I mentioned yesterday).
Either way, a scan leads to a new tab where VirusTotal's dozens of anti-virus engines kick in. When they're done, you'll know if it's safe to download the file (or visit the site).
I'd say VTzilla is a must-have for security-conscious Firefox users. It's free, easy to use, and potentially a lot more effective than the AV software residing on your PC.
Not a Firefox user? Check out my original coverage of VirusTotal, which still allows any user to e-mail or upload a suspicious file for scanning.