Yes, but not in the way you think!
Short answer: All that matters is the pips and level of the mod, and NOTHING ELSE.
Long answer: The way pilot power is calculated is by taking the pilot's Galactic Power and multiplying that by whatever bonus (or malus) you get from the star rating of their ship. So anything that increases the pilot's Galactic Power will increase the stats on their ship. When you equip a mod you gain an amount of Galactic Power that depends on the level and quality of the mod, maxing out if it's 5-pips and level 15. The rarity of the mod, the stats on the mod, the set bonus it gives, none of that matters at all towards your Galactic Power, so it also has no effect on your Ship Power.
So the easy, practical thing to do for a pilot you don't plan on using elsewhere is to farm up a whole bunch of gray-quality mods, level them up to 15, and throw them onto the pilot regardless of what other stats they give. Just give them something and you're good to go!