I'll take on your question with some personal knowledge. I got picked up by an agent in an unusual fashion, without tons of querying. The agent had a particular new editor in mind when she took it on. So your scenario, while not common, could happen. So, what then?
My wait for an agency agreement took about two months. The agent was working to sell the book while I was waiting, so I didn't really notice. A formal offer on the book (with multiple discussions in the middle) happened four months after the first initial discussion with the editor. It was an email to the agent with the potential terms. Then negotiation ensued while the terms were countered for more money, better promo, etc. We were lucky in that in the meantime, another publisher had made an offer. Once the terms were finalized, the actual contract arrived about five months later. However, once again, as soon as a verbal/email acceptance was made, everything started moving forward as though a signed written contract was done. That's pretty common in the industry.
The publisher decided to add the book to the launch of a new imprint, so things moved unusually quick after that. We had an edit letter about three months later. We had two weeks to complete a near full rewrite of portions of the book. The copyedits arrived about six weeks later and again, we had two weeks to make corrections. Same thing with galleys. Six weeks and then two weeks to proof read the final copy. The cover and back copy and such were happening in the meantime, so that the final book hit the shelf in about eight months.
I don't recommend this pace for major publishers. It's actually pretty daunting to fit it into your life because you have to create on command. That takes practice. Two weeks slips by so amazingly fast. I much preferred the second book's schedule, when I had four weeks to make any major edits.
I was fortunate in that my first book, with a small indie publisher, was also on a fast timeline, so at least I had a concept of what was coming from the Big 5 pub.
The epresses I've worked are generally missing the galley level of edits. It's also become easier to edit with email and Track Changes in Word than the paper edits I got when I started.
So, figure in the best case no less then eight months and possibly up to sixteen months from acceptance by an agent to release. It can also happen it takes years to get an agent and more years to find the right publisher. It all depends on your book and the market at the moment. Good luck!
