Maybe. For small battle I don't use one, I just use dice on the table to illustrate where everyone is.
I get out the battle-mat for large scale battle, but in the future I see myself using a whiteboard.
I need an "I got them seared into my mind/process during 3e and 4e, so I'm currently using them, but I'm desperately trying to remember how to run TotM" option.
I voted yes, but not physical battlemats I use roll20 for all my gaming and on that I use maps with 5' grid sections just like I do for Pathfinder and 4e.
I'm going to try going without, probably using an A4 drywipe board for general terrain illustration, but may revert to using them if it proves difficult.
As long as the more complex grid-based combat rules can live side-by-side in the same game as pure PHB TotM stuff, I'll be pulling out the battle-mat only for big set-piece encounters where terrain and positioning play an important part.