We have a small area of ply pipe boxing in our kitchen. It has 24 x 4" tiles on it, and they are all "stuck" on with "No More Nails", and grouted with flexi grout. We have had no problems at all.. Ours is a permanant fixture though, but i'm sure the same method of fixing etc to your moveable " ply pipe boxing" would work too..... It was convenient for us to do it this way,,,, but saying that,, there are proper flexible tile adhesives and grout for using on plywood. If it is the correct thickness and type of ply (WBP) and it is firmly fixed (screwed) into place, there should be no problem.
Roughcaster.