It varies. Everyone does some background checks, and some do very in-depth ones with lots of “off sheet” references (i.e., ones not provided by the CEO).
Many do few references checks outside of the CEO.
The most important thing is address any issues up front.
Due Diligence for most VCs is meant to be confirmatory. Just to confirm things are expected. Usually, by that point they’ve either decided they likely want to do the deal, or in many cases on background checks, may have even already given you a term sheet on the assumption the checks work out before the deal closes.
Finding material issues late in the potential investment process is a big flag.
So disclose whatever issues there are early. Maybe not in the first meeting. But probably at least before the third.