Chomsky normal form method: CYK parser performance implications?
While the obvious answer is that the fundamental complexity can't change, there may be better or worse algorithms for parsing the strings you're actually going to encounter. However, it seems like the issue is less the relative frequency of individual grammar productions (the A's, B's, and C's in the question) and more an issue of the unused, dead end parses that one binarization versus another may produce.

With a bit of searching I found Better Binarization for the CKY Parsing (Song, Ding, and Lin, EMNLP 2008), which seems to definitively conclude that you can pick a "better" or "worse" binarization relative to the strings you actually expect to have to parse. Their name for the "dead end parses" that one would hope to minimize in practice seems to be incomplete constituents, and there is a good example on the first page.