No, for making it so that the rest of the team doesn't have to deal with emails from 7am to 1am.

Part of the PM's or manager's job (at least if they're a good one, anyway) is shielding the rest of the team from administrivia, so that they can be productive.

sure. try to be the first point of contact for a massive project for anyone under the sun including fellow developers, business users, IT heads, business heads, internal consultants, external consultants, SMEs etc etc. If you can handle all their queries (email/in-person/phone call/video conference), you certainly sir do not need your BA/PM.