I have updated the main post with v1.1 which should detect root a bit better. I am still interested to hear of results with other devices. If there are issues I may be able to create device specific patches that can be applied in the same way.
No change in behavior with my rooted, custom De-Odexed TW ROM for Galaxy S3.
I do have ADB enabled but it doesn't pop up & request root privs on my unlocked, open desktop of the phone.
Of course, my TW doesn't need it because USB-DAC works fine as-is.
I am looking into the driver situation now, just out of interest what is the codename for your NA S3? (eg i9300, d2vzw, d2att etc)
Mine is a D2att. Which is the North American Galaxy S3 for AT&T.