Traditionally wainscoating is nailed to blocking installed between the studs to give it a solid installation........You don't have the necessary nailing surface to install it correctly........Is the top of the baseboard a square edge?..........
Installation depends on the thickness and quality of the wainscoat.......Construction adhesive......and nailing the top and bottom moulding MAY work........But if there is any warp you have no way to straighten the work..........