Assume the Republic Senate voted for some kind of inquiry to determine if the Supreme Chancellor had acted legally and if there are grounds for impeachment (for example, bear with me here). Even if Palpatine speaks the truth to any question and made no attempt to hide anything, even his Sith identity, would his executive decision to invoke Order 66 be considered legal nonetheless?
First, does the Jedi Order have the legal power invested in them for Mace Windu to do what he did, or is it considered extralegal? Based on the legal definition of Order 66, does Mace's actions fulfil the conditions necessary to legally invoke it? And does Palpatine have the executive power to unilaterally invoke Order 66 without consulting or getting approval from any entity?
Second, would it matter to the Senate if Palpatine had come clean about his Sith identity as the reason for the attack? Does the Senate consider Sith to be enemies of the Republic by default like the Jedi do? Would the Senate have considered the Jedi's actions legally justified solely on the basis that Palpatine is a Sith? For that matter, does Palpatine have enough public popularity and political support to influence the Senate to turn a blind eye anyway and vote in his favour?
To summarise: Even if Palpatine made no attempt to cover up and just spoke the truth in any questioning, was open about his Sith identity, and did not use the Force to manipulate the Senate's minds, would the laws of the Republic, the Chancellor's legally granted executive powers, the wheels of democracy and the dirty game of politics ultimately work in his favour anyway?