You should be able to, yes.
It will look like a digitally compressed POS compared to a quality HD satellite/FIOS feed... and especially compared to Blu-ray Disc.
But, it should work.
I say should because some projector manufacturers may not deliver as they are supposed to. None that I am specifically aware of though. I have had good luck in testing HDMI with all of the projectors I have used with Blu-ray Disc.
Worth saying that many of the cheapest, business class, projectors I have tried have looked absolutely terrible with video. They looked okay with data, but not with video.