The Rejector's been a bit busy as of late. If you are ever are considering converting to Judaism, make sure to ask about Passover/Pesach in great detail. Don't let the rabbi leave out the part about how much work it takes to clean your whole house out and cook for special week when you can't eat normal food. Yeah.
Without knowing I queried what turned out to be an agent assistant at a very prestigious agency and she asked me to email my entire novel. Would it be safe to say she is eyeing my book for one of the agents she works under? I don't think she has any clients, and has been at this large agency less than four months. I would guess you must have to put in at least a year or so before you can rep clients, right?
There is no standard for when assistant agents who are taking on clients are different from regular agents. The line is very wavy and not really relevant to you at all. All you need is a person who is going to take your manusript, edit it, care about it, promote it, sell it, and make sure the publishing house sells it. Whether they have "senior" or "assistant" in front of their agent title is irrelevant.
And as far as how assistants work, I would think you guys especially want to keep your to-do pile in check. From what I've read it seems you and your boss reject quickly, but I've heard many response horror stories. In my case the assistant has had my ms for over two months and just responded to my "checking-in" email to say stay patient and that she will get through it asap. For all I know she might not of read a single page. But overall, assistants are probably more on the ball, right?
A good assistant who has been hire to do the mail will do first-level rejections basically same-day, though same-day may be "the one day a week the assistant comes in." Either way, rejection is fast. Acceptance is slow. Three chapters doesn't take long to read. I can read a stack of partials in less than an hour. Then a full - even if I read it fast, that doesn't help because the agent has to read it and make the final, crucial business decision to put their time and money behind the project. That's a major decision and is made carefully. So there's really no way for me to answer your question, except to say, assistants are paid hourly, so we are expected to get the job done.