Frankly, any aliens able to travel here from another world are so far ahead of us, it wouldn't make any difference if we detected them or not.
However, you asked the question... so...
Our space detection system is largely aimed at Earth. For example, to warn of us of ICBM launches the first system put into space was called MIDAS between 1960 and 1966.
http://en.wikipedia.org/wiki/M...
The GPS satellites have nuclear detonation detectors, which doesn't do any good, but it another example of how our systems are aimed at Earth.
All the stuff pointed out into space, like the Hubble Space Telescope, are designed to see VERY far away and aren't looking for ships. Given the small likely size of any ships compared to planets and moons, we aren't likely to be able to see them even if we're looking for them, until they are on top of us.
After all, we still don't have a telescope that can see the moon landing sights. Pictures taken from sats in lunar orbit have gotten some pictures, but they aren't as good as you'd expect.
http://en.wikipedia.org/wiki/T...
This is the best image I could find of Apollo 11's landing site, and this was after the LRO was moved into a lower orbit:
http://featured-sites.lroc.asu...
Yea, you can tell what it is, because you know what you're looking at, but if you didn't even know where to look? You could stare at the moon for a month with such a camera and see nothing.
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TL;DR - We likely would have no notice whatsoever of aliens until they entered orbit of Earth, and even then, it is just as likely to be a random person with a telescope who spots them as anyone from the government.
Unless of course they can be seen with the naked eye, if their ships are big enough and they are in low orbit, that is possible.