The checks and balances is based on who is in the office performing the particular check and/or balance, and in most cases by far it is the Republicans themselves who are in the position of doing the checks and balances, because the US constitution is so naive and antiquated that it doesn't consider partisanship, but assumes that everyone would consider their office first and political affiliation last.

So no, they can't do those checks and balances because they are not in a position to do so.