What this achieves is not a center channel but a difference channel which might best be placed in the rear. It is a variant of the "Hafler" circuit.
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For a center channel, one wants to have only those signals that are common to the left and right channels. (It's a little more complex than just summing but similar.)
However, by connecting the speaker between the two hots means that current will flow only when there is a voltage difference between the two hots. Thus, it will reproduce a difference.
Playing and placing such a speaker between the left and right will not fill the middle but, rather, increase the effective separation.
Yes, you will get a difference signal, and if you have inverted one stereo channel signal, this difference signal is indeed the common mode component of the stereo signals and is what you want to drive the center speaker. Of course, you must connect the speaker of the stereo channel that is inverted backwards so that its audio output is properly phased.
I used this kind of center channel drive for many years, with the signal inversion being done by hooking up one channel of the phono pickup backwards. This is far and away the best way to derive a center channel from a two-channel amp.