In the 2001 version of CEFR, the descriptor for "phonological control" for level C1 simply read,
Can vary intonation and place sentence stress correctly in order to express finer shades of meaning.
Of course, a learner at level C1 has also passed the lower levels. The descriptor for level B1 says,
Pronunciation is clearly intelligible even if a foreign accent is sometimes evident and occasional mispronunciations occur.
And for B2:
Has a clear, natural, pronunciation and intonation.
The descriptors were updated in 2018. Instead of a single descriptor for "phonological control", there are now three categories: "overall phonological control", "sound articulation" and "prosodic features".
The descriptor for "overall phonological control" for C1 says (my emphasis),
Can employ the full range of phonological features in the target language with sufficient control to ensure intelligibility throughout. Can articulate virtually all the sounds of the target language; some features of accent retained from other language(s) may be noticeable, but they do not affect intelligibility.
So if "poor pronunciation" means that intelligibility is negatively affected, then you can't have level C1 if you have a poor pronunciation.
The descriptor for "sound articulation" for C1 says (my emphasis),
Can articulate virtually all of the sounds of the target language with a high degree of control. He/she can usually self-correct if he/she noticeably mispronounces a sound.
So if "poor pronunciation" means that a learner usually does not self-correct mispronunciations, , then you can't have level C1 if you have a poor pronunciation.
The descriptor for "prosodic features" for C1 says (my emphasis),
Can produce smooth, intelligible spoken discourse with only occasional lapses in control of stress, rhythm and/or intonation, which do not affect intelligibility or effectiveness.
Can vary intonation and place stress correctly in order to express precisely what he/she means to say.
This goes beyond mere correctness of pronunciation: you need to be able to vary intonation to express things such as surprise, doubt, irony, etcetera. A learner who is not able to do this cannot claim to have reached level C1.
Note also that the 2018 version of the CEFR no longer uses the language of a native speaker as the "gold standard"; in the CEFR in general "native speaker" was replaced with "other speakers of the target language" or similar phrases.