The expansion properties of polyurethane glue could indeed address the challenges posed by less-than-perfect Domino joint fits. It's a valid point that polyurethane glue doesn't rely solely on wood-to-wood contact, offering potentially stronger bonds.
The application process you've described, using an acid brush and a wet paper towel for wrapping, seems efficient and focused. This could potentially save time compared to the traditional method of applying PVA glue to both the mortise and the Domino.
For those interested in delving deeper, https://www.meiboom.eu/epdm-lijm/ could offer additional insights into specific glue types. It's always beneficial to gather a range of information to make informed decisions about the materials and techniques you employ.

I would note that I used polyurethane glue once.  It was a difficult piece to clamp, so I used a bungee cord for that purpose.  An error.

The glue expanded and partially opened the joint. 

If you are going to use polyurethane glue, make sure the joint is securely clamped.