Boehner wouldn’t be elevated to VP if Biden left. Obama would get to nominate a replacement, subject to Confirmation under the provisions of the 25th Amendment.
If Biden resigns then Obama follows suit without a VP in place, Boehner becomes POTUS.
Nixon got to nominate a replacement V. P. because Agnew was forced to resign before Nixon resigned.
If Obama were impeached, that would be it for him.
Biden would nominate his own V. P. Of course that’s if Biden didn’t drown on his own spittle before Obama left office.