Can I use AppleScript to delete files on NAS listed in a file?
As an alternative to using AppleScript, it is so much easier just to do it in Terminal using bash, e.g.:

while IFS= read -r line; do echo rm "$line"; done &lt; /path/to/untitled.txt


Run it as is with the echo command to have a look1  at its output, and if it look okay, then run the command again without echo in it.

Note that when run without the echo command, the path file names will be quoted, so while with echo command will show as e.g.:

rm /Volumes/Multimedia/Music/ITunes Media/Kiko/Come On Up/Come On Up.mp3


However, without the echo command, the rm command with the path file names will execute as e.g.:

rm "/Volumes/Multimedia/Music/ITunes Media/Kiko/Come On Up/Come On Up.mp3"


Thus handling path file names that contains spaces.



1Hint: Enlarge the window in Terminal so you see the full line without it wrapping on the screen as this will make it easier to see any anomalies, if any.