Hi there,
I have quite a few tracks with Tempo and Time Signature changes. Is your Click MIDI? If so the MIDI should drive the master tempo/time signature and therefore any Arps/Sync’d effects etc should … sync!
See here; Time Signatures & Virtual MIDI Input for Media Playback
If it’s not MIDI then I can’t help other than suggest you try the method of adding the MIDI track (and write your time signatures etc there)