avast does not scan webmail, no AV does.
However if you download a attachment it will be scanned

Gmail have already scanned the mail for you, they protect all accounts with Postini spam filter that is using twin AV engine to check for virus. McAfee/Authentium
Yahoo use Norton
Hotmail/live mail use TrenMicro

If you use a mailprogram and download the mail to your comp, then you can sett up avast to scan it…