If someone told me that the spoke conversational English then I would expect their speaking level to vary. Also, I would expect to hear plenty of informal English with some formal English in their speech because that's what conversational English consist of. So, if someone told me that they speak conversational English I would definitely not expect to hear any academic language(still possible), but I would expect to hear some type of informal English and formal English varying from a novice level to a native speaker's level of speech.

Thanks for answering, Carvin! But "varying from a novice level to a native speaker's level of speech" is why I asked this in the first place. I'm wondering which end of that spectrum people take it as.