Yes, you can think of biological entities as algorithms, but that doesn't give you any explanatory power.
Unfortunately, most people have little to no understanding of algorithms, and how little actually constraint is imposed on something when you say it is "algorithmic". In particular, there is no restrictions on algorithms that require them to be deterministic. When theoretical computer scientists talk about pseudorandom number generators, they are talking at a much higher level of rigour than any biologist, psychologist, or neurologist ever uses. From their point of view, unless the biological entities you are thinking about are trying to defeat each other's cryptosystems, all random or stochastic events in biology can be viewed as pseudorandom with absolutely no consequence for biological theory. In fact, Keegan's answer that we can think of stochastic events as deterministic events with a mechanism that is outside of our model scope would be equivalent to the worry of pseudorandom versus true-random numbers.
Even if you subscribe to the (silly) Penrose-Hameroff stance that quantum effects in microtubles have a macroscopic effect at the level of consciousness that leads to "true randomness" then that still wouldn't place you outside of algorithmic thinking. You would just have to think in terms of quantum algorithms, which is more difficult mathematically, but a well studied field of computer science. Finally, cstheory extends the notion of algorithms beyond the typical confines of randomness as studied by statistics and most scientists, and looks at rigorous models of non-determinism.
In fact, there are people (for example, I advocate algorithmic philosophy as an extension of standard analytic philosophy) that believe that any communicable theory is inherently algorithmic and ammendable to analysis of cstheorists. Hence, not thinking of something as algorithmic would be impossible.
That being said, is that useful? In general, no. Algorithms are incredibly difficult to study. In the case of the computing machines, we make it easier by separating the algorithm underlying the physics of the hardware from an abstraction that we call the software. This often leads non-cstheorists (as you can see in Keagan's answer) to thinking that the idea of algorithms applies only at this "software abstraction" level. Of course, this is not the case. However, this distinction can be a useful metaphor at times, and much of cognitive science is based on the idea that the mind is software that is at least in principle capable of being implemented by different hardware. This is the philosophical stance of multiple realizability.
Neuroscientists hold this stance much less often, and - as suggested in Keagan's answer - view the mind and brain as non-seperable and best analyzed at the same level. This does not make the process non-algorithmic, it just takes away any handles we have at easily isolating properties of this algorithm.
If we continue this idea further, and just consider an algorithmic black box then we return to the ideas of behaviorism that are now considered passe in the cognitive sciences, but still popular in many parts of biology. In this setting, the black-box algorithm is a correct but completely useless notion. We have mathematical theorems that tell us that if we try to treat algorithms at this level of abstraction then we can never (in general) conclude anything. In this case, we have to be more restrictive than just "algorithmic" or "computable". This can get us to fun cstheory questions like "What is the complexity class most closely associated with what the human mind can accomplish quickly?"
