Will Wood Glue Stick To Polyurethane . In fact, if you are looking to bond end joints of word together, then. The wood glue has chemicals that will soften the polyurethane finish, which will allow the glue to stick and bond to the wood. Wood To Concrete Adhesive from www.walesfootprint.org This means that the glue will not dry completely on the surface of the object before it is removed. It forms a very strong, water resistant bond. The short answer is yes, it will stick to painted wood.