The Han Unification problem arises from the inverse case - characters that are used in several languages but rendered differently depending on locale[0]. For those characters, they'll render even without a pan-CJK font, but the problem is they'll render in a way that's not appropriate for their locale.
[0] Another way to phrase this would be "distinct characters which share a code point becaus Unicode mistakenly thinks they're a single character whose rendering differs by locale". The difference is basically subjective.