Can the "Acting" Attorney General enact new regulations?

A thought crossed my mind after reading a few lawsuits brought by parties alleging Acting Attorney General Whitaker is not the proper person to be the Attorney General under the law. In fact, a few senators filed an action in DC District Court, Blumenthal, et al. v. Whitaker, et al (1:18-cv-02664) alleging, among other things, that Whitaker cannot be the Attorney General and that Rod Rosentein should automatically assume the title until the President appoints, with the advice and consent of the senate, a new Attorney General.

There is another case, pending the United States Supreme Court, which makes similar accusations that Whitaker is not the proper Acting Attorney General (Barry Michaels v. Jefferson B. Sessions, et al). Why does this matter? Well, there is a rule regarding bump stocks that the Department of Justice and Bureau of Alcohol, Tobacco, Firearms and Explosives will be "final ruling" shortly. From what I gather, the Attorney General is required to sign these rules. Loretta Lynch (previous Attorney General) signed the last ATF rule (https://www.federalregister.gov/documents/2016/06/13/2016-13878/recordkeeping-regulations) and more recently, then-Attorney General Sessions signed the proposed rule for bump stocks (https://www.federalregister.gov/documents/2018/03/29/2018-06292/bump-stock-type-devices).

What happens, then, if the new bump stock rule is "final ruled" with Acting Attorney General Whitaker's signature, and then his appointment is later to be found invalid/unlawful? Does this bump stock rule (and more broadly, any act he would have taken as Acting Attorney General) become void? I don't know enough to say one way or the other, but I am following both the Supreme Court case and the DC District case cited earlier very closely. Stay tuned for further updates.