Yes, TimeBolt will read multiple audio tracks in an MP4 file. You can select to include all or choose which tracks to ignore.
If you filter native in TimeBolt the file will be flattened into a single audio track with the ignored audio re-synced after the cuts are made.
If you export via XML into Premier/FCXP or EDL into Resolve, all audio tracks will be imported and can be modified as separate tracks but newly synced to the cuts.
To manually remove silence cuts via XML/EDL, upon opening TimeBolt, go to ‘File’ —> ’Settings’, and opt to keep all cuts where you can manually delete silent tracks inside a supported NLE.
See video hub for exact instructions for Premiere and FCXP: https://www.timebolt.io/video-hub