[Sleuteltje]

Would that approach work within the Kodi API/infrastructure?

No, it would not.

I think I have it working, I just kept trying until it would accept my settings.  I now have a TV show playlist I can manage.  

Good to hear . What was the cause of the issue? In case someone with your problems comes along.

One question - Do I leave the timezone set to default or do I need to set my timezone in GMT?  
Thanks

The timezone setting is meant for offsetting the update time if its in another timezone. Example; lets say you yourself are in GMT+1 and you are following a youtube show that states "new episode every wednesday at 15:00 GMT+2", you can then set the timezone setting of the playlist to "GMT+2" so you don't have to calculate what 15:00 GMT+2 is in your timezone (GMT+1). Hope that clears that up.

One more question - I notice I get an updating Youtube library message when I restart Kodi. Does that mean that it will start downloading shows if I restart? (I don't want that).
Thanks

No, it shouldn't. Unless you have stated that it should. There are 2 sort of intervals, one for checking if playlists should be updated (this will run every X amount according to how you set this in the addon settings, default is 30 minutes). This the "updating youtube library message" you are reffering to. Every playlist has a setting of its own on when it should be checked for new videos. If you have left the notification addon settings at default, you should also see a updating message for each of the playlist individually every time the addon will check for new videos for that specific playlist.

OK, TV shows are being downloaded now (approx 5pm PDT). I set the interval to daily, the time to 3:00, and the timezone to default.
Is that because I need to change the default time or is it because I restarted Kodi?

Could be a number of factors. Could be the time on your computer is wrong, you have a wrong timezone set in the addon, wrong playlist settings etc.
If you have set the interval for checking the playlists to slow it could be it was just doing its first run of checking playlists at 5:00 pm. Thats why you should let the checking interval run like every 30 minutes max. and set in every playlist when they should be updated. To not have that be a tedious task, you can set default settings for newly created playlist in the addon settings (in the tv, movies, musicvideo tab accordingly).

Also, I don't get any sound when I play the files. Is there a setting I need to change?
Thanks

You said you set YTlibrary to download the videos? There should always be sound. Which playlist / video is this about?