I wonder whether such experiments were conducted? Is it possible to create a "biological super-computer" this way?
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This is actually not an unheard of idea among neuroscientists and is an aspect of much research. Brains in general have amazing computational powers and abilities that allow them to circumvent the limitations of computation which is usually based on a Turing Machine. Neurons pursue highly parallel architectures and exhibit cognition or even emotions or do highly sensitive signal processing, which has heretofore been unapproachable with computational methods such as Machine Learning.
As such many researchers are focused on understanding the brain or at least the brain's structure to augment or produce computation. Here are a couple of examples of neuron arrays flying virtual or real drones....
The ethical issues aren't great concerns because neural cell networks can be encouraged to grow differentiating from easy to grow cell lines like fibroblasts.
Another approach to augmented computing is to interface directly into a living brain. Model brain organoids are a popular topic of interest and could one day be used to interface to other computational systems. There are of course many devices that try to interface to the brain via electrical fields in the same way EEGs work.
there are connectome projects that are trying to understand the neural connections between cells that are so important to brain development, with the theory that the topology of these networks might enable even computers to perform like brains.