No, it is not affected so far.
According to contingency plans for the Office of Personnel Management (OPM) (which the National Background Investigations Bureau (NBIB) currently falls under), the NBIB is not funded by annual appropriations and its functions will continue during the government shutdown.
Category III. The majority of OPM’s employees perform functions that are funded by sources other than annual appropriations. These alternatively funded functions would continue during a lapse in appropriations under the “multi-year appropriations and indefinite appropriations” exemption cited in the Justice Department’s 1995 Memorandum.
Specifically, OPM operates four activities pursuant to our revolving fund statute, which are funded by agency fees and other payments. These include the National Background Investigations Bureau (NBIB), which operates OPM’s background investigations program, and Human Resources Solutions, which provides services to agencies on various human resources issues. While the vast majority of these employees work in NBIB and HRS, several employees in other parts of OPM are also directly funded through the revolving fund, because they provide essential services to the NBIB and HRS operations.
Each of these revolving fund activities currently carries an operating balance that will allow its functions to continue even in the absence of further agency payments during a lapse in appropriations. In the event of an extended shutdown, however, the ability to continue some or all of these functions would have to be reevaluated. It is theoretically possible that funds from some of these revolving fund activities may not last throughout a lengthy shutdown. In that event, we would re-evaluate whether the functions would fall within a separate exception to the Anti-Deficiency Act’s prohibition on incurring obligations in advance of appropriations.
(emphasis mine)