One of the biggest problems with AOHell was their use of proprietary applications.
However, in this case it entirely depends on what application is used to view the emails. If an AOHell email client is used to convert from webmail to email, I doubt it would be scanned as it is unlikely to be using standard POP/SMTP protocols.
If the AOHell mail is viewed through your browser (provided that isn't an AOHell proprietary browser) then the avast web shield should be monitoring the normal http traffic when you view your webmail through your browser. What is your browser ?
Any attachments in your email would have to be saved to your hard disk and they too should be scanned either by the web shield or the file system shield (when they are saved to the hard disk).
So up to a point you should be covered by avast (over and above what Pondus mentioned), it all depends on the applications you are using to view the webmail.