Sorry, but this question is fully based on speculation. How can one even expect an serious answer on this one?
Point is: to ask the question, you need to speculate on what an alien invasion would be. You even need to speculate further to provide an answer. What's that worth? What do you learn out of it? How do I know if I can detect and observe something if I have no Idea what it is?
I could tell you, for example, that we will definitely be able to see the aliens come because of the huge gamma flash their flying saucers produce when they drop from hyperspace nearby Saturn. Our detection change is 100%. Or is it? My answer here is worth nothing, because I have to speculate to what an alien invasion would be. I could sit down with scientist, military analysis et politicians for week and make nice action plans based on what-ifs, but it would all be a waste. Why? Because we simply don't know anything about this topic.
A more serious question would be the same, but replacing "alien invasion" by "potentially hazardous asterioids". Now you can start an interesting discussion because you know what asteroids are and which one can be classified as hazardous. You know what you can observe and what you can't. Knowing the detection limits and methods, you can start to discuss about blind spot and detection probability. Going further you can even talk about mitigation, worst case scenarios and post-impact solutions. On this one I'd gladly sit down with other experts.