If a ton of them offer
banana: ) at approximately the same time, then yes, you will probably get your pick. If there is high interest from multiple parties, the agent SHOULD initiate an "auction" where each publisher submits sealed bids and then the agent will try to up the ante with each of them to find you the best overall deal (not just necessarily the best money, but the best terms overall.)
However, what often happens is that one or two will offer right away, and others will be slower. That has happened to us. We got just one offer on the initial round and took it. Right about the time it hit the shelf the following year, another publisher FINALLY got around to reading it and wanted to deal, then just this past week a
third publisher called our agent and wanted it (it's now been
on the shelf for nearly A YEAR!)
With any luck, we can sell the other two publishers something else, since they liked the first one.
But yes, it
can happen, and I hope it does for you.