I doubt it. Certainly, I wouldn’t.
This is an appointment that the Democrats will want to make into a big issue. The best way to remove it is to put the imprimatur of a “respected” Democrat lawyer on the choice.
Cabinet secretaries make independent decisions, even when following the agenda of the President. All Gorelick is asked to do is to ratify a choice that the President-Elect wants to make, and supply legal authority for that choice. It is better to take an opponent lawyer to validate a controversial decision. She is not being asked to advise anyone in the Trump administration, simply to state the legal basis for a decision made.
Why would the Democrats do anything to obstruct the appointment of a guy with no political track record who comes from a family of major Democratic donors/fundraisers?