Going back to the original question, we don't know if you are talking about acrylic/latex water based products and/or solvent based products. Painting with a broad brush/generalities, with top coats it is generally safe to put a latex product over oil based, but not vice-versa due to the differing expansion/contraction properties (I hope Demarpaint agrees?). This might not apply to primer/sealers because they are built different than top coats (resins, pigment, etc.).
If I were to try your method, I would thin the (assumed solvent based) polyurethane about 50:50 with mineral spirits and wipe it on with a rag. It will penetrate and seal the wood. It might raise some "fuzzies", but it is always recommended to lightly sand the sealer/primer (maybe tack rag) prior to top coating. You could force dry the car in the oven (not so hot that pine resin comes to the surface).
Is the top coat going to be rattle can?