I agree with a combination of the answers above.
There are a lot of factors that impact when you should hire Account Managers, their role, and what the transition process from AE to AM should look like.
That said, my preference is introducing the Account Manager to the prospective client later in the sales cycle, but not necessarily waiting until the deal is closed. (Per Bonnie's comment)
The transition from AE to AM is very delicate. Each deal typically takes months to close, and in that time, the prospect gets more and more comfortable with their AE. The idea of exchanging that trusted comfortable relationship with a brand new one is stressful. Including an AM in the later stages of the deal eases the prospect (soon to be client) into the transition.