It's not only possible, but is done every day in the painter trade.

You do not need to remove the poly. It only needs to be dull.

Wash the surface with Dirtex and wipe dry. Be sure all grime and grease is removed.

Sand lightly with #180 aluminum oxide sandpaper. Dust and wipe clean.

Prime with Zinsser Bulls Eye 1 2 3 or BM Fresh Start. Both are water based, acrylic primers.

Topcoat with a high quality 100% acrylic or urethane acrylic enamel.

Pro Classic. Cabinet Coat. Impervo. Muralo Ultra. All are good products to use.

Michael

Do you also need a primer if there is only oil-based stain on wood (no poly) and you will be using a very dark-colored oil-based paint?

Yes. I would prime whether using alkyd paint or acrylic paints.

You can prime with the Bulls Eye 1 2 3 acrylic primer and coat with the alkyd paint. Yep. You heard me right.

Michael