I e-queried Barbara Poelle on March 21 and received a repsonse from an agent assistant, Georgia Johnson, on May 31. I don't ever remember getting an auto-reponse, but I won't swear to that. I would say that if you don't hear anything after 12 weeks, requery.
I don't think it'll do much good to query another agent at this agency with the same letter. It sounds like once the query is received, it's reviewed by the agent assistant(s) before being passes along. So it's likely the same person will be reading the same query. However, if you have a slightly altered letter, I'd send it in.