It is illegitimate with or with out him.
The constitution gives them no power to impeach a person who is not a sitting president.
I'm not sure about that, impeachment in England developed in the 1500s to give the Commons a way to BLOCK appointments by the King because they had not yet acquired the power to control who was in the government. So, initially, most men who were impeached were NOT sitting officials. The men who wrote in 1788 "The House shall have the sole power of impeachment" surely knew this.
However, it does not matter in this case because Trump was impeached while he was a sitting President, and the Constitution specifies,"the Senate shall have the power to try ALL impeachments".