That's true. But can someone who is not eligible to the Office of President, be "a President"?
If he's not President, he can't be impeached, but then again, he would not need to be. He'd need to be escorted gently out of the White House, and into federal lockup on fraud charges, pending other possible charges.
[I’m no lawyer to let you know.]
I don’t consider him to be a legitimate president. Unfortunately, he was processed in and sits in the Oval Office. So, best I can tell, he would need to be impeached.
To me, this is one of those important moments that defines the DNC more than anything else.