You are correct. The House will certainly have the power to investigate and subpoena all relevant documentation, which is what most of us would like to see, not necessarily impeachment.
The main problem with impeachment, of course, is that while impeachment requires a simple majority in the Republican House, conviction requires a 2/3 majority in the Democratic Senate.
They couldn’t get a majority vote in the Senate against Clinton when it had 55 GOP Senators!
Boehner may be afraid to find out the truth. I think that the American people deserve the truth, though.