The problem is that when you need diversification the most, in times of economic and financial stress, the correlations between asset classes go way up, and that can include high quality corporate bonds. That is what happened in the financial meltdown. Almost all asset classes were almost seamlessly correlated - in the downward direction. Heck, my high quality short term corporate bond fund dropped close to 15% as I recall at one point. That was pretty sobering.
You mean, +?
If by "+" you mean, was the correlation was positive, the answer is yes, since they all moved "in the downward direction."