It'll chase the false localizer, behavior of which is a little unpredictable, but most times I've seen people report it'll do 360s repeatedly, maybe with some course reversals mixed in. It's not a pre-programmed response, it's naturally coming from the plane's simulation of the localizer radio signal propagation. You should guide yourself in HDG or LNAV onto an intercept of 30 degrees or less, or better yet, all the way onto the final approach course. Unlike other aircraft, because ATC says "cleared approach" doesn't mean you must/should arm APPR and/or switch to "green needles" manually. It's ok to use the FMS as long as you've switched to using the localizer passing the FAF (or if ATC explicitly say to use the localizer before that, like they often do at LAX, for example). Some more information from irl Challenger pilot and one of our consultants: