Yuck, that's definitely not one I would want. I'd suggest a Panasonic PT-AE8000U, it's a great projector. If you are tight on budget there are cheaper ones that are decent, just be sure it has decent native resolution, good amount of lumens balanced with a high contrast ratio, ideally both horizontal and vertical lens shift and a short throw lens would be good if you don't have a huge room to work with.
It won't have any effect on FPS, it's just the display it's not doing the work. I used to watch movies and play games on a Sanyo PLV-Z4 all the time, it was great. Not super bright though, I needed to ensure there wasn't a lot of light when I used it.