Yes, moving your full fleet in alerts them, and all adjacent planets..
If you do sufficiently small strikes it might not alert the planet and not adjacent ones, meaning you can go under the radar for a while, if you however destroy any vital building (command station) then all other adjacent planets go into full alert...
But besides that more ships you have, does not mean more ships for the AI. the Reinforcements of the AI are something calculated from Progression + Difficulty + Planet Count * Player Number (i think something like that ,p)
So.. more planets will cause more reinforcements, more progression and higher difficulty too, and every additional player doubles the threat. ^^