Can a center channel output from an AVR be run serially to 2 bookshelf speakers?
Technically you can, but, as others above have already commented, there are good reasons why two speakers should not be run per channel. Most likely, one speaker per channel was the intended design.
In addition to those reasons, when two speakers are run serially, the second speaker gets a different signal than the first one. Nearly all speakers have voice coils as part of their electromagnetic motor, and these coils have inherent inductance not unlike the inductor coils in their crossover networks. So, the second speaker will get audio signals that have passed through additional filtering that the first speakers were not exposed to.
To make matters worse, the voice coils move according to the audio signal, changing their inductance as they move. So the second speakers get varying audio signals, depending on the audio content.
Don't hook up speakers in series to one audio channel. It probably won't cause any damage, but it won't sound right.