Indeed so. You are correct. I don't know why you got so downvoted. // Remember that for many of us who are
not from the northeast, we "can't" have a lax vowel like /æ, ɛ, ɪ, ɔ, ʊ/ in front of phonemic R. Those all get neutralized so that we have "only" tense vowels like /e, i, o, u/ (or also /ɑ/) before R. That’s why I said I've heard both /o/ and /u/ there in
/pɑɹˈkuɹ/ and
/pɑɹˈkoɹ/. I think
turd though has what they call the NURSE vowel, which is more centralized and highly R-colored. —
tchrist ♦ 1 hour ago