God Mode and Full Shield don't work as expected for the player's capital ships.
My finding are based on flying my first, and newly built Argon L Destroyer-class Behemoth (believe or not, I haven't cheated money at all, very proud of myself
).
Full shield doesn't work whatsoever, whether I'm flying the cap-ship personally or letting its captain take control.
God Mode works in that it prevents the cap-ship's hull from taking damage (stays at 100% while option is checked). However, the ship's modules are still vulnerable to damage.
I picked a fight with a lone enemy cap-ship of the same size (Paranid L Destroyer-class) with the intention to board for a war mission, but my engines and most of my turrets were destroyed before I could finish the selections in the boarding interface.
Whether there might need to be an additional/separate option for cap-ship God Mode to account for modules, I don't know. But so far, the table's God Mode barely works with cap-ships and Full Shield doesn't work at all.