Nope. This is the one I saw: http://www.youtube.com/watch?v=HHcHYisZFLU
For the casual viewer (who is not a huge Alien fan or already aware of Prometheus) there is nothing in the trailer that says "Hey! This is a film about Alien!"
The trailer does heavily rely on imagery from Alien, such as the cryo-beds, the derelict, a cavern (not with eggs, but with strange cylinders), and a brief scene towards the end with a character screaming "Get it off!" as he has something attached to his face. But your typical movie-goer who has never heard of this movie is not going to immediately connect those things with Alien unless the trailer ends with a xenomorph sticking its tongue out.
EDIT: The video nick_danger posts is different from the one I saw in the theater, but my original point still stands. Anecdotal, but I turned to my friend and she didn't know it was an Alien movie. I'm sure I could show the trailer to a dozen other friends who would all also not pick up on the similarities.
I'm not trying to take anything away from this movie; I'll probably do everything I can to convince my friends to go see this with me.