If you have Count-in enabled, you should hear it regardless of whether the metronome is enabled for recording, but it might depend on your interface driver - possibly you need to have a track with input monitoring enabled to keep your interface 'awake' when the transport isn't running, and/or make sure you have 'Always Stream Audio Through FX' enabled in preferences.
IIRC Project > Insert > Time/Measures will move meter/tempo changes along with track content, but not markers. Slide over to Make Room is only applicable to pasting, but it has long-standing issues (see the ReadMe), and should not be used.
EDIT: I just double-checked... even with 'Always Stream Audio Through FX' disabled, and no Audio or Synth tracks in a new project, the count-in is audible with just a MIDI track armed.