I've used acrylic paints over nitro (with more clear nitro over the top), and that was fine. As it's water based, there shouldn't be anything in there to react with a polyurethane finish, and a lot of car spray paints are acrylic based (so should be 100% compatible) so there's a 99% chance you won't have any problem. But as has already been said, for 100% peace of mind, spray a test piece of wood first and try the acrylic on that, and then spray the clear coat over that. I'd give each stage a couple of days to dry thoroughly before putting the next type of finish on.

You're probably best sanding down the original white paint to maybe P600 rather than leave the spray finish as-is before the acrylic paint goes on, so it's got something to key into and not just sit on top of a shiny surface.

Make sure the clear coat is the same type of paint type as the base coat, preferably from the same range by the same manufacturer.

The amount of clear you'll need to spray for a flat gloss finish depends on how thick the acrylic paint is applied. If it's thin and smooth, you'll need to apply enough of it to match the level of the acrylic, and then probably 6 coats more to give enough depth to sand flat and polish without risk of sanding through to the acrylic.