Did you have any particular type of attached document in mind? Some need specific (and often proprietary) decoders.

Actually, in some situations, Thunderbird can't even search the body of emails, so searching attachments seems rather unlikely.

Answering Zenos's question: I just need to search through doc and pdf files which are attached to Thunderstorm emails. (By default Thunderstorm does not search automatically inside any attachments for a keyword.) Is there any way to make this search for a keyword automatically through all emails including also inside attachments? Thank you.

I suspect that both of those would have licensing issues, since they are formats owned by other bodies. Note that Thunderbird itself doesn't even offer to preview these types of files, but hands them off to other applications. So it doesn't know how to read them, let alone search them.

How do you normally search doc and pdf files?