I'm quite sure it would work. Buildings are completed at the end of your turn. Then the AI acts In Between Turns. So, you palace would complete before you lost your old capital. Probably a good idea to have enough cash (or an engineer) on hand to rush it.
(only) If you control the oceans.
That sounds hard to reinforce, no cultural defense (or easily bombarded away by ships), and accessible to amphibious invasions.
Hill is good. Far from attackers is good. Hard to reach is good.
Island in the middle of a lake sounds good, but it didn't work for Montezuma.
One turn before you finish palace in city A, you can deleted it from your building queue, then build it in city B. But the hammer you invest in city A is NOT lost. You can finish palace in city A anytime. If you follow me, that mean you could change capital to any of your city if you prebuild.
BTW, TheMeInTeam, who is your avatar, what is she doing?