Of course there's a difference. A thinner, less sturdy baffle will vibrate more sympathetically and create it's own antiphase addition to the tone creating a signature chara... PLEH!!! I just barfed a little in my mouth.
The tonal difference almost certainly won't be significant. More significant is how the baffle thickness affects the fit of the grill board in the recess. You'll need the depth measurement for that to know if it's a problem.
P.S. The thread title is misleading. "Baltic Birch" is plywood. "birch" is wood wood.