They have a very difficult job and it's refreshing to them to deal with thoughtful individuals. Acknowledging them as people with their own goals and dreams makes the job a bit easier. Jessica, a subagent at a smaller agency, appreciates it when someone she's talked to sends a note thanking her for her attention. Assistants also may be your ticket to success in the future. They also remember the writers they loved and the agent didn't.
Agencies have different methods of handling the mail and scripts.
In some agencies, the standard practice is to open the mail daily. I've heard about one agency where the agent, subagents and the assistants collect all the letters once a month and sit around a table reading them and as a group decide which scripts to ask for and which to reject. Also, I have not heard of an agency where answering the mail is anyone's only duty. Query letters are silent slips of paper that can simply be dealt with later when there is time. Contrary to how you may think, they don't enjoy rejecting people, so it's not a task they leap to do.