Yes, if you wish you can use any instrument as a click track. Just record or draw in the notes in a region and loop it.
This would be useful if you couldn't alter the sound of Logic's click track.... but you can ;-)
Either Control-click on the Metronome icon in the Transport Bar or File > Project Settings > Metronome...
and change the tonality/note, etc and choose when you hear the click the track.
Open the Mixer, Choose to view All Channels and on Inst 256 you should see the Click Channel with the Klopfgeist instrument (literally, this is German for 'knocking ghost').
In the Klopfgeist you can choose various presets (e.g. kick drum short, pluck, tonal etc or create your own favourite click track sound!