My Cato colleague Bill Watson says no:
Many will argue that you need fast track to pass free trade agreements, but right now trade promotion authority is largely useless and unacceptably costly. Recent history with fast track shows that the obstacles to passing free trade agreements depend more on the partisan and ideological balance of Congress. Imposing Congress’s policy objectives into the negotiations at this stage won’t help get the TPP accomplished any sooner, and will surely reduce the value of the agreement as a vehicle to liberalize trade.
A clean fast track bill that reduces the role of controversial non-essential objectives in the TPP negotiations would do wonders for the U.S. trade agenda. Unfortunately, Congress seems poised to insist on making the TPP an even more "ambitious" agreement.
The president has options to get the TPP through Congress that don’t involve the risks that come with a formal grant of trade promotion authority. If he wants support for the TPP, President Obama should listen to congressional leaders, adapt his negotiating goals accordingly and then lobby Congress to pass the agreement once it’s completed.
Basically, his point is that Congress can, if it wants to, vote up or down on a completed trade deal even without fast track, so mucking up the process with fast track now doesn't really add anything.