Yes. In Wedge's Gamble, there's a passage that talks about the main computer centre and says something along the lines of
Rumour had it that if the Death Star had been used against Coruscant, the computer centre would have been a recognisable and salvageable piece of debris.
Wedge's Gamble, p243
which suggests that the Death Stars' superlaser would overwhelm even the double shielding in place over Coruscant.
As to the point about Tarkin and Vader, as I said in this answer Vader was on the Death Star precisely to prevent Tarkin from getting the idea of taking out the Emperor. The Emperor also organised the leadership aboard the Death Star (between Tarkin, Tagge and Motti) so that all three would be jockeying for power between them instead of working together to do something ... foolish.
I guess even Vader couldn't stop the leader of the battle station do what he wants
Well, if Tarkin had gone off the rails and despatched the Death Star's entire stormtrooper garrison to take out, frankly my money'd be on the dude in the black.
BTW my reading of Qui-Gon's 'I can't fight a war for you' statement is less a reflection of his capabilities and more to do with the neutrality of the Jedi.