The reality is a little different. The FBI Director serves at the pleasure of the President, and legally speaking Trump could fire him at will.
While that could materially interfere with Congress’s ability to be properly informed on an issue (since a disrupted investigation might be prevented from producing evidence), the reality is that wouldn’t affect whether Congress could use its impeachment power. The constitution offers guidelines for impeachment, but it’s basically left up to the Congress. If a majority of the House agrees to impeach, and then 2/3rds of the Senate votes to convict, the President is removed from office. Thus most people acknowledge impeachment is ultimately a “political decision.”
Since it’s a political decision, the political ramifications of the President using executive branch authority to interfere with an investigation that might implicate him, would be very bad, probably so bad it could result in the President being impeached.
The one good test case we have of this is from Watergate. Nixon decided the Special Prosecutor Archibald Cox was a problem, and ordered his Attorney General, Elliot Richardson to fire Cox. Richardson refused, and then resigned as Attorney General. This made Deputy AG William Ruckelshaus acting AG, he was also ordered to fire Cox and refused, and likewise resigned in protest. So finally acting AG falls to Solicitor General Robert Bork, who considers resigning instead of firing Cox, but ultimately goes along with it and fires him.
This really backfired pretty substantially. A Federal court ruled the firing to be illegal (but there was no immediate remedy.) More importantly, public opinion was big, and for the first time significant numbers of Americans began to support Nixon’s impeachment. This was known as the “Saturday Night Massacre” (it occurred on a Saturday in October 1973), this also soured Nixon’s relationship with many congressional Republicans. Due to the immense public and political pressure, Nixon was pressured into appointing a new special prosecutor, Leon Jaworski. While there were many more twists and turns between the massacre and Nixon’s resignation in August of 1974, his actions here did him no favors. While I’m not sure Nixon could’ve ever survived Watergate, his firing of Cox definitely did him no favors, it turned more of the country against him in a lasting way, that made people question his honesty and integrity.
Since he was pressured into appointing a new special prosecutor, the firing of Cox also produced little material gain in Nixon’s quest to try and weather the Watergate storm.
I think we’d see a similar thing with Comey’s firing, except right now there has yet to be a true “smoking gun” incident directly linking Trump with Russian election meddling. So if anything, firing Comey at this point could serve as the first step toward both the public and congressional leaders seriously considering impeachment, so it could actually be worse for Trump than the Saturday Night Massacre was for Nixon.
It’s also worth noting that just like firing Cox served little strategic purpose, firing Comey would likewise serve little purpose. The meat of the investigation is being done by career civil servants, whom the President cannot fire at whim. If the President fires Comey, is able to appoint a new FBI Director who is a yes-man, and the FBI director orders the career civil servants to cease their investigation that would be an unprecedented political interference in the workings of the FBI. That in itself, like firing Comey, would build significant support towards impeaching Trump for abuse of power, even without clear evidence linking his campaign to Russian election meddling.
So basically:
- Yes, Trump can fire Comey
- No, it wouldn’t stop Congress from impeaching him
- It would probably make impeachment more likely than if he doesn’t fire Comey