That won't work since your NAS is not part of C:. What you'll probably need to do is map the network drive to a drive letter on your computer. (For instance, I have my NAS set up as P: on my computer, and MusicBee can see it.) I strongly recommend only having one machine handle the organization, if you have MusicBee on both. Otherwise they could get into a tug-o-war over the files.
And yes, if you add the drive as a monitored folder then "check for missing or updated files" should find new files for you.