I'm sure it's possible, you can talk to  MattBo about lucid dreaming. It can get frightening aswell.

I have a bit of knowledge on the subject as well as sleep paralysis.
What specifically do you remember about the dream?

I remember there were aliens. Like aliens you would see out of Gears Of War.

Well, how long ago since your last gaming experience with Gears?

Like, four years.

Thought about them recently? Seen anything to spike interest? Played the soundtrack recently?

No no and no.

It's been more about Amnesia recently.

Well, hmm.

as far as distorting the real world, I don't believe that would be possible... however, distorting the dream world is very much so possible, I do it all the time in my lucid dreams... it requires quite a bit of practice to really master the dream world and all it has to offer, but yes, ANYTHING is possible when you dream. I have had the same situation that you described with false awakenings before, I'd wake up and be half way on my way to work and then wake up in bed again and I'd be like "wait wtf??" lol

but I recommend you use caution when tampering with lucid dreaming, because you can and most probably will get sleep paralysis when you wake up from a lucid dream, and sleep paralysis is by no means an enjoyable experience.

I remember the first time I've experienced sleep paralysis.

I was in a constant state of panic even though I knew I was in absolutely no danger at all.