In canon, Dumbledore claims that Voldemort's soul latched onto Harry's soul, which means that this would work. Dumbledore is very smart and knows much more about magic than I do, so I think that it would probably work.

Latching onto Harry's soul doesn't prove that mutual horcruxes would work since it doesn't address my example of destroying horcruxes one at a time, and I'm pretty sure Dumbledore nowhere says that the mutual horcrux scheme would work.