Can I add a window AC in a house with central AC (old rental house, poor insulation)

Please ELI5

I rent. The house has shitty insulation in the attic, plus old windows. The central AC unit functions okay (but with lack of insulation, it just can’t keep the house cool “enough” — especially the bedrooms). So, would it make any difference to add a window unit in the bedroom – would it help to keep that room cooler? Or am I screwed without better insulation?