Yes, but keep in mind the wall color will effect the image color that you see. This unit is very bright, so ideally you'd want to shine onto a flat finish white or light grey wall. PS4 won't be a problem. It won't be full HD, but will scale and still look nice for the price.
If you're really into your gaming, you're going to want a high end projector in the $1000+ price point. Something that can handle higher resolutions (at least 1080p)--this one will be showing 480 (I can't remember if it's progressive scan or not). So your PS4 will be capable of giving more than this can handle, but the processor in it will scale it down to give you a nice enough image to use and feel like your $300 was a good investment to start off with.