Some life forms seem likely to be able to survive that kind of ejection, and a long trip through space, and re-entry in a planetary atmosphere [2].
If we find life on the Moon, or Mars, or Europa, it could turn out to be that it originated on Earth. It would still be an amazing and extremely interesting discovery, but not the momentous discovery that finding true alien life would be.
When considering the possibility that Earth life has spread to other parts of the solar system, one should also consider the possibility that it went the other way. Just as ejected material from Earth can reach other planets, ejected material from other planets can reach Earth. Some believe that conditions on Mars once were more favorable for the origin of life than they were on Earth, so it is a possibility that life started there, and then spread to Earth. Around 0.2% of meteorites found on Earth are thought to have originated on Mars.
[1] http://arxiv.org/abs/1108.3375
[2] http://www1.univap.br/~spilling/AB/Olsson-francis_cockel_201...
Needles to say, we live in a society where many base there beliefs on blind faith, and those who do are almost impossible to convince of something that goes against their faith. Even if simple life was found on the moon, they wouldn't believe it unless it was the kind of alien life from movies that invades earth with spaceships.