I've read that once intelligent life successfully achieves interstellar travel, it could populate the galaxy in tens of millions of years, likely populating the most habitable planets and preventing the development of intelligent life there.
Unless two civilisations achieved this at roughly the same time, its unlikely to have two forms of intelligent life in a galaxy.
So whilst it's unlikely there's intelligent life in our galaxy (because if we weren't the first, we wouldn't be here) it's quite possible that alien civilisations have populated other galaxies, and there are hundreds of such candidates less than 10 million light years away.
The question is, if a galaxy was populated with alien life, would we notice? Would the radio waves and other unique life like signals coming from millions of populated planets be detectable, or at interstellar distances would it be so small as to be undetectable noise?