Is an impeachment actually likely to get him out of office?
Probably not (at least not directly), since republicans in the Senate are unlikely to vote him out.
Or is it just an inconvenient media/legal circus that ties down the accused during proceedings?
Trump has been a very corrupt and destructive individual.
Impeachment proceedings can do 3 things (any of which will be beneficial)
- It might force him out of office. (The chance is tiny, but it still exists)
- By highlighting some of his corrupt behavior, it gives added knowledge to the electorate in the next election, so that even if he's not forced out within the next year, there is a better chance he'll lose in 2020.
- It may help 'tie him down', if Republicans decide that the added attention of impeachment necessitates them actually cracking down on Trump.
Now, there is a chance he may become more unstable over time, but given how bad he was before, I can't really see things getting much worse.
No presidency has ever been ended by this procedure, right?
Nixon resigned, but he would not have left office were it not for the impeachment proceedings.
Would it not just feed the -already substantial- persecution fantasy of Trump's base and energize them for the elections?
There is a chance that some people who might have liked Trump are encouraged to vote instead of sitting out the 2020 election. But there's also a chance it will energize people who might have sat out thinking "Trump ain't so bad" to make them think "Ok, this guy really does need to be removed".