I would say yes as the most logical way for the soul to control the body is with the proteins that are able to form prions and RNA that behaves similarly, because they are in all life, spread out, are essential to life and intelligence while having no identifiable mechanical use, etc.
Anyway does scripture or any guru have something to say about this?
There is a famous shloka in Chandogya Upanishad that states that all is Brahman.
Sarvam khalvidam Brahman ...
Verily, all this universe is Brahman....
Chandogya Upanishad 3.14.1
So it follows naturally that viruses, prions etc are also Brahman. There is, however, a difference between them and sentient beings. Brahman is Satchidananada. Sat is the principle of existence, chit is principle of consciousness and Ananda is the principle of bliss. Brahman is existence itself, consciousness itself and bliss itself. In the case of viruses, prions etc the consciousness and bliss aspects are veiled and only the principle of existence operates.
The key ingredient in soul is it's chetna. It is "able" to cause action (karma) be it physical, physiological, psychological, social, etc.
So to test whether the virus/ virod / prons have souls we have to observe how are they behaving are they being able to "act".
The most visible type of karma for these kinds should be movement, if they move even in their prey host cell "independently" from the environment then they have souls else don't.
To be able to detect independent movement at that lengths would be difficult.
We just had discovered the Brownian motion and it is at much greater lengths, to the length of viroids.--- Research required
Now second thing that may indicate some action would be chemical (physiological) changes in them, i.e. mutation in these cases, which according to my knowledge is not done by itself.
According to Viroids video of Sci-show viroids can (a) preserve info and (b) catalyse reactions.
I think viroids are like dead bodies they preserve info and catalyse reactions. In the RNA world they may have been alive either they are parts of dead cells or have their own origin through natural selection.
In case of origin through selection they have souls, in case they are parts of dead cells then they don't. And we can also see their conscious movement for final determination.
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