If there were intelligent life in another galaxy, would we notice? 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?
 A: To answer such a question you need to set some parameters. The obvious thing to do is to ask whether, with our current technology, we could detect ourselves at the distances you suggest?
The answer is no. You can find some more details in the related question Detectability of interstellar messages
In summary, the most powerful radio signals we send into space are from the Arecibo planetary radar. This is beamed radiation - into a solid angle of about $6 \times 10^{-7}$ steradians (a few square arcminutes). The Arecibo dish could detect its own signal in 1000s of integration from a distance of about 5000 light years (Cullers 2000).
The nearest other galaxies (e.g. the Magellanic clouds) are about 20 times further away, so would require 400 times more power in the signal.
The detection of such signals would require us to be looking in exactly the right direction (the beam is very narrow) and at the right frequency at the right time. There is no obvious way that the signals from different star systems across the Magellanic clouds (which are hundreds of beamwidths across) could be combined to enhance the detectability of a beamed signal, other than to make it more likely we would be looking in the right direction.
In terms of the more general radio noise our civilisation emits; we wouldn't even detect that one light year away. Thus you would need to add up the signals from $>4\times 10^{10}$ such planets to get a detectable signal and there aren't even that many stars in the Magellanic clouds. Even if there were, the addition of such signals would have to be done in some common, coherent way in order to produce a detectable signal rather than a mish-mash of radio noise.
