Does 가래떡 mean "phlegm rice cake"?

 ANSWER: No, it means "a stick of rounded rice cake."

I have read that some younger Koreans think that 가래떡 is a vulgar way to refer to "stick rice cake" because when they think of 가래, they think of "phlegm" or "sputum," not "stick," but 가래 can also mean "a piece" or "a stick" of something, as in 가래떡 (a stick of rounded rice cake) and 가래엿 (a stick of rounded taffy). And 가래 is also used as a counter word for stick rice cakes and taffy, as in 엿 두 가래, which can translate as "two pieces of taffy."

From Dong-A's Prime Korean-English Dictionary

From Dong-A's Prime Korean-English Dictionary