I think it's very unlikely that there was an explicit connection intended, beyond making the acronym pronounceable.
Wikipedia includes various accounts of the origin of the term, which all agree that the original requirement was for an abstraction layer to handle input and output (frequently abbreviated as I/O) in order to release CP/M on a variety of hardware platforms. This concept is more generally known as a Hardware Abstraction Layer, or HAL, but since the discussions were all about I/O, the name "Basic I/O System" seems to have just been the obvious choice. The fact that other components of the system have acronyms which don't remotely resemble Greek words suggests that there was no culture of clever references in the CP/M team at the time.
Only later did the term come to refer to the more complex firmware that controls a PC's boot system, which I suspect is what you are thinking of as "analagous to a biological system" (although I still don't see the connection myself). At this point, it was just an earlier term being borrowed and applied to a new technology with some of the same purpose.