Yesterday I finished playing the tutorial. I had a fleet of 6 invasion ships. During the first couple of rounds invading the first Xeno system the ships took damage, but after that they took no damage. Then they took no damage during successful invasions of the two remaining Xeno systems.
Not one point of damage, that just didn't seem right..
I was planning on using that game to test my new invasion ship designs, but that didn't provide enough data, so I've started a new game. I'm on a bigger map (38x100?), but with the new zoom-zoom UI, it may not take too long for me to get to invasions.