Yes, you can use PVA to size a painting surface, but ensure that it is a pH neutral, archival size to avoid deterioration further down the line. A good product to use would be Gamblin's PVA size.

The main issue with using PVA instead of a regular acrylic primer is that you will end up with a very glossy surface to paint on, with no 'tooth', which makes it more difficult for the paint to adhere.