Sometimes. From what I've read, some portions of your vision aren't working properly, though you are technically "awake." Human brains are very adept at filling in missing information, whether it's text or pictures or vision. So it just supplies an image that would kind of make sense.

I've seen some convincing arguments that this might actually be the original source of the stories about succubi and incubi. (One of the other common symptoms of sleep paralysis is that the whole genital region is one of the "awake" parts of the body). People saw (or rather, didn't see) a big blotch right in front of them, got startled, and their brain provided an image of a demon attacking them as something that might reasonably fit in that kind of situation. Nowadays there are fewer people who think that "demon" is a valid explanation for anything. But you still see similar stories about alien abduction. The people who claim the experiences are usually pretty insistent that it actually happened to them. And in a sense, they're right: they were actually awake, their eyes were actually seeing what they were describing, and their brain did actually interpret the stimuli to produce the (understandably frightening) image they're remembering.

Personally, I had one episode of sleep paralysis when I was a kid. The "blotch" was on my wall - I thought it was a pile of black ooze spreading out, and is probably still the creepiest thing I've ever experienced. My parents thought it was just a really realistic nightmare. But when I was in college, I found out about sleep paralysis, and was completely sure that's what it was. A couple of years ago, my daughter had a similar experience; she saw it as a "piggy shadow" that scared the pants off her. I was able to help her out right away, since I knew exactly how real she thought it was. I was around 5 years old, and my daughter was around 4, and we both still remember the experiences extremely clearly. So, yeah, they make a pretty big impression.