Will the under table mount turnout switches work with 1/4 inch plywood table top with 2 inch styrafoam layed on top of it.
To some extent it depends on what type of switch machine you are using. But I dont think there are any stock switch machines that reach through 2 1/4 inches. However, all is not lost. It would be very simple to extend the throw with either styrene or stiff wire.
It depends on the turn-out machines you’re using.
Tortoise machines are slightly more than 2" tall, so they will stick through the bottom of your benchwork requiring a hole in your plywood.
Atlas and Peco machines are about 1" tall or less and won’t extend below your foam.
In some cases it is easy to cut some of the foam from under the turnout. Mount the turnout machine on a piece of thin wood or styrene. Glue this in place under the turnout. this makes a good solid base and puts is at the right depth. making adjustments are easier to do with a solid backer.
You can easily substitute the rod that comes with a Tortoise switch motor to make it longer using a piece of piano wire, which can be purchased at most Ace Hardware or similar stores.
I have used piano wire up to 5 inches long on some Tortoise machines and they still function perfectly.