Using Content Taxonomy where existing content is already tagged with core's Taxonomy module

no, there is no easy way to do this upgrade. content taxonomy fields use there own tables for saving, so you would have to save all terms to the content taxonomy tables too.

I've got a related question.

Content Taxonomy question: I have nodes already tagged with Vocabulary terms using Core's Taxonomy module. If I replace the Taxonomy field in my content type with a Content Taxonomy field and enable "Save values additionally to the core taxonomy system (into the 'term_node' table)", Drupal's Taxonomy table(s) will remain up to date, correct?

If this is the case, I could use the widgets provided by CT to improve the end-user experience and use the core Taxonomy fields when configuring Views filters and displaying related Vocabulary terms for that content type. Is this correct?

Just looked into this myself and I think the answer in "No" because, while Content Taxonomy will keep Core's Taxonomy term_node table up to date, it will wipe away already existing entries for a given node the first time a term is entered.