I’m not sure, but I think I have the definition of a throw away line down. Were throw away lines more common in older movies? I just saw Some Like It Hot this weekend and one that immediately springs to mind is this line:
Now is this considered a throw away line? How is a “one liner” different? If a rimshot would fit in after the punch line is that a way to determine the type of joke?
I can’t believe nobody’s mentioned The X-Files yet. David Duchovny (Mulder) was the master of mumbled throwaway lines–half the time he’d improv them during rehearsal and they’d put it in the script if they liked it.
Two that I remember offhand, both involving the Lone Gunmen:
Byers: We’re dealing with the most heinous and evil force of the 20th century–
Mulder: Barney?
Byers: --(finishes the line, can’t remember what it was)
Langley: Hey Mulder, wanna [insert insane LG scheme here]?
Mulder: I’ll be doing laundry…
spit take
I didn’t see that show, but that cracks me up too. 
I would say it’s not. I haven’t quite hashed out a difference between a one-liner and a throwaway, but this joke has a clear setup and punchline. A throwaway is something extra. If it had gone like this:
SUGAR: Yes. I come from a very musical family. My mother is a piano teacher and my father was a conductor.
JOE: Where did he conduct?
SUGAR: On the Baltimore and Ohio. [Beat] They had a symphony orchestra on the train, it was really nice.
…that might be a throwaway. The joke (obviously) works without it so it’s okay if you miss it. But if you do get it, it’s that much funnier.