The only problem with staining it is that poplar and birch plywood are usually pretty different looking as far as grain goes, and they will accept the stain differently…. possibly even exaggerating those differences. Still, us woodworkers love the look of wood, so stain always has a leg up on paint. :-)
If you do decide to stain with a water-based product, be sure and follow the directions to use a conditioner first to minimize grain raising. Also keep it mind that a dark stain will require more than one application, in all likelihood, to achieve the look you are seeking.
If it comes out looking awful, you can always go back and paint it.
-- Charlie M. "Woodworking - patience = firewood"
