Does the existence of one species imply the existence of many other?
I am not sure I'm providing the kind of answer you would expect.

Your question is very conceptual. For such question it is important to very well define the concepts you're using. For example, the concept of species is not well defined (and will certainly never be well defined as it does not represent a natural category to my point of view). Also, the separation you do between complex and non-complex species might not be obvious. For example, you create two categories which are bacteria/virus and multicellular. But you kind of forget the many of the eukaryotes which belong to non of these two categories. Or some bacteria that might almost be considered as multicellular.

I think it would help answering your question if we had the arguments of Sir Arthur Clark for saying such things. Below are two arguments I could use to defend your statement.

Speciation:

If you consider than one population rarely (or virtually never) go under sufficiently major changes before undergoing speciation, then you would never have only one species which is very different from the others.

Ecology:

One might consider that one species cannot by itself be responsible of a whole cycle of elements. Therefore, if the species we observe can theoretically live forever (equilibrium), then, it implies that other species must exist to recycle their wastes. But this hypothesis has nothing to do with the separation of species per complexity that you do.



Update:

Following your comment: So what you had in mind seem roughly the same than my "Ecology" argument. The difference is that I emphasized on the fact that one species alone cannot live for ever because they degrade their resources through time. I did not want to say that one individual of one species cannot live without the presence of another individual of another species. This individual would need the presence of the other species not for himself but rather but its great-great-grand-children when one resource would have been totally consumed by the ancestors.

For your curiosity, here is base of the tree of life. What is eukarotic but not plants, animals or fungi are called protista and are all (or almost all?!) unicellular. You'll notice that viruses/viroid and prions does not belong to this tree. It would be a bit long to explain why they are no represented and it would have nothing to do with your question :D