Impeachment doesn't mean you're federally barred from office, nor is it a requirement for someone to be federally barred from office. The two things are separate. As I said before, one of the arguments being made for pursuing impeachment is that it would be a useful fact-finding exercise if you were looking to bar him from office. This could be achieved in other ways and since he is being investigated in several states and now DC for inciting a riot in the Capitol, not to mention any federal crimes he may or may not pardon himself for, and the fact he has faced an impeachment trial already in his term, I wouldn't say another attempt is crucial to this aim. Not to mention, as I pointed out, it is nigh on impossible for a impeachment trial to be conducted within a week (the House could vote on Wednesday, the Inauguration is a week on Wednesday).
It's a clever line, but lacks any understanding of the American political system. There are not 18 Republican Senators who entertain thoughts of running for President in 4 years time. There were 17 candidates in 2016 and only 5 were Senators and one wasn't even still in the Senate. Add to that that 74 million people voted for Trump 3 months ago and regardless of the events of the past week, you're going to have to convince a lot of people who voted for Trump that you deserve the nomination. Voting to impeach their leader is probably not your best strategy for winning the nomination. Finally, what right-minded Republican Senator wants to try and pick their way through the civil war that is about to engulf the Republican party and try and form a winning coalition in 2024?
In short, there are not going to be 18 Republican senators who will vote to convict Trump, even if there were it wouldn't bar him from office, and even if it did, the Senate won't hold an impeachment trial this side of Inauguration, after which time I doubt they'll bother anyway.