The likely strangeness of any non-terrestrial replicators, along with the fact that it's likely we'll be wondering whether they're intelligent (or even "alive" and self-directed) make the typical scenarios of alien invasion fiction seem a little quaint. Contact with alien life that results in predominantly poor outcomes for Earth life - an "invasion" is likely to seem more like an extermination effort on their part, or the by-product colonization by non-native organisms, like kudzu.
It probably won't look much like Independence Day. It probably won't look "military" at all, in the sense of the aliens it/themselves, or our response to it. (I appreciate that most people would rather pay to see Will Smith in a dogfight with aliens than a nuanced exploration of the ecological impacts of contact with alien life, but I think there is still an audience and place in independent films for this, though this one wasn't it. Come on guys!)
Of course, I'm assuming we would even notice anything is going on. Mammoths no doubt noticed the first humans wandering down North America's west coast from Alaska, but whether they were able to comprehend the existential threat of a new superpredator along with climate change is doubtful.
But we're not mammoths, you say; we have language and writing and tools. So how could we not know what's going on, and what the effect will be? Yes, we can accurately claim that we're at the top of the cognitive pyramid in our own biosphere. Just because that's true does not mean that we've magically come to some plateau where, because we can understand more things than other vertebrates, we can understand everything. There's an enormous amount of chutzpah in that assumption. There are no doubt dots that humans can't connect, just like there are dots the mammoths couldn't connect. A mutation in FOXP2 in the late Lower Paleolithic didn't suddenly make us into all-powerful general comprehenders. Polynesians watching European landing parties row to their shores weren't able to really figure out what was going on, and they were dealing with members of the same species, separated by only a few millennia of technology. If there are in fact any replicators moving outward from the galactic center, they've possibly been using tools for millions of years longer than we have. (Still not convinced? Try figuring out a quipu or cuneiform and then leave a comment. And those are "primitive" technologies, again from your own species.)
Alien invasion films are fun, but they really look a lot more like movies about fighting funny-looking humans with technology from a few centuries in the future. After all, the U.S. military now has Martian heat rays. The key will not be how to stop alien invaders. The key will be recognizing what they are in the first place, and what impact they will have on us. Talking philosophy with them is a long-shot. A zebra mussel once tried to argue with me about Hegel and it was the lamest conversation I ever had.