You can treat a large organism as a superposition of quantum states. However, in such large systems there are many many many interactions. The result of treating a large organism as a superposition of states, and using the quantum time evolution function quickly results in a set of states which, if measured, would be tremendously correlated.
If you wanted to calculate it, the power tool you would want would be the Central Limit Theorem, which states that if you take draws from a random variable (measure the state of your organism), the distribution you draw from becomes increasingly normal and the standard deviation decreases linearly with the number of measurements.
As many of the interactions within an organism are well-modeled as classical (meaning we made sense of them without resorting to quantum mechanics), these interactions act as measurments in this sense. Thus your virus, with its 4 million atoms, will quickly converge on a easy-to-analyize average behavior with a statistical deviation of perhaps 0.0000001% within microseconds. Why do I choose that percentage? Well, in the physics community, a certainty of 99.9999% constitutes a "discovery" that is so unlikely to be due to random chance that the community is okay with ignoring that likelihood.
In other words, the behavior of a virus sized object in normal thermal conditions is so predictable by looking at the mean behavior, that you could claim that a virus does that behavior (as opposed to saying there's random variance around that behavior), and be credited with a "discovery" in the physics community sense.
Now if you had a large object in a known quantum state, you might be able to interact with it in a way which exhibits that quantumness in a way that wasn't predictable classically. However, this is an extreme corner case. We don't know how to put such a large object into a specific quantum state with current technology, and the particular interactions which exhibit this behavior (rather than collapsing back onto the classical behaviors) would be narrow indeed.
We currently do not believe large organisms need to be modeled in that way, although there are a handful who argue there may be small-scale quantum behaviors in the brain.