Rushing the capital is always a strategy as even if the computer player senses the attack, it cannot move all of its forces because they lack the transport capacity required. And it might be even the only thing to do if they are much more powerful than you.

That being said, when you conquer the capital like that, then all of the former GP's lands become available to be invaded by all computer players. They don't even need to declare a war (it is not possible anymore anyway). So there is a risk that GP's lands get shared across other GP's, although they did nothing to earn them.

Therefore, if possible, I first annex their colonies and then eat out their land and take the capital at last. But I see that this strategy is not always possible, especially in early game.