Yes there should be no problems playing your MediaMonkey playlists, I do it all the time.
A little concerned about cancelling the db errors and still carrying through with the install, it may have ramifications for the operation of MonkeySqueeze amongst other things.
Anyway, just to confirm the operation of the system, it works like this. MonkeySqueeze enables MediaMonkey to play music on the Squeezebox system. With MonkeySqueeze enabled when you start playing music in MediaMonkey, the Squeezebox system will play the same music.
Steps to follow
1. I would uninstall MediaMonkey and reinstall by right clicking on the exe file and selecting "Run as administrator"
2. Reinstall MonkeySqueeze by running MediaMonkey in Administrator mode
3. Re-enter details in the MonkeySqueeze options page
Check the following:
1. Make sure MonkeySqueeze is enabled. Button on the main toolbar menu; turquoise for enabled, red for disabled
2. There should be no information entered in the "Logitech Media Server on a NAS using Linux" section. No boxes checked, no music library addresses
3. The Squeezebox device that you are linking to (The one with MAC address on the Options page) must be selected in "Choose Player" drop down box (top right corner) of the LMS web page, otherwise no music will play on the Squeezebox system
4. Double check all settings on the option page against the info on the LMS web page > Settings > Information tab
Try all that, and if no further success then post back.
Cheers
Gingernut63