The simple answer to the question in the title of this post might be considered to be, "Yes, genealogy is complicated." But it is helpful to understand what we mean when we say something is "complicated." There is a whole area of study called "complexity theory" which extends to strategy, economics, complex systems and includes areas such as chaos theory and computer related topics such as computational complexity theory. See Wikipedia: Complexity theory.
Looking at the topic of complexity from a very simplistic standpoint, we can detect many levels of complexity. However, there is no universally accepted definition of exactly what we mean by complexity. I began thinking about this recently when I was talking to a person who was explaining a very convoluted family relationship involving the historical practice of plural marriage (aka polygamy). The person doing the explaining seemed to think that the issues involved some high degree of complexity, however although I said nothing about the situation, I thought what she was explaining was quite simple and not out-of-the-ordinary type of issues commonly faced by genealogical researchers. She was using the excuse that the family relationship was "so complicated" that there was no way the genealogical relationships could be properly researched and so she was not going to do any further research. I think I smiled and said I would be glad to help her if she wanted assistance.
Genealogical research definitely deals with a "system." In addition, we are dealing with a system of limited relationships rather than a complexity of random relationships. Although there are variances in the any ancestral system, there is certainly a rather limited number of possible combinations of elements (individuals related either culturally or by blood or marriage). Since we are dealing with a system of organized complexity, we can predict that current patterns of relationship extend into the past, that is, unless our ancestral families came from an area with a distinctly different culture than the one we presently live in.
Genealogical research does, however, involves a complexity of elements. The study of this type of complexity is usually associated with network theory. One graphical representation of this type of social or ancestral network is the program called Puzzilla.org. Here is an example of a screenshot showing a graphic representation of some of my ancestral relationships.
FamilySearch.org Family Tree and is only as accurate as the source information. In addition, this is a two dimensional representation of a multidimensional system. Many of the people represented by node (dots) in this graphic had more than one spouse. Some had many spouses. But this particular diagram only includes those direct family line individuals that have been selected by the user (me) as the preferred lines. But it is a good place to start in understanding the complexity of doing genealogical research. Each of the generations increase the number of direct line ancestors by doubling the number in the preceding generation, i.e. you have 2 parents, 4 grandparents, 8 great-grandparents etc. In addition, you add in the multiple marriages and all of the descendants and you get large numbers very quickly. It is this rapid expansion into rather large numbers of relatives that makes genealogy appear complex.
In addition, each of the individuals represented above and all of the other spouses, children and collateral relatives of each, could be the basis of extensive research. In a very real sense each person could potentially be the subject of a long and detailed biography. As genealogists, we often arbitrarily either limit or discard information that exceeds our interest or the "scope of our research." If we did not do that, we would all be involved in writing extensive biographical works about our parents or perhaps, our grandparents.
When you think genealogy is complex, you are really comparing it to other systems that may seem to be less complex. Actually, genealogy is not very complex by any absolute criteria. Genealogical research is repetitious and examines each node in the system (each ancestor) with the same or similar set of basic criteria. For example, I believe that I am advancing with my genealogical research as I fill in the blanks in an arbitrarily designed genealogy program. When I feel satisfied that I have enough information about any particular person, I move on to another person in the pedigree construct. This is essentially a repetition of the what I just considered to be finished. The appearance of complexity comes from the multiplication of these basic systematic units, i.e. families. Of course, I am not limited to biologically bases family units, I can add in adoptive units, foster units, and so forth.
What did the lady referred to above mean when she expressed the idea that her polygamous family was complex. She was, in effect, comparing that particular family to some idealized family unit that did not have as many variations in the relationships. However, as I pointed out above, there is no absolute measure of complexity. But even on a relative scale the variations in the relationships of individuals in an ancestral system cannot be considered to be very complex on any absolute scale. Complexity at this level is usually a result of a large number of random associations. A truly complex system is based on a large measure of unpredictability. This is not the case with genealogy. The system is regular. Alternative familial relationships, such as adoption, foster care, etc., merely add additional, yet similar, nodes to the general outline of the system.
None of this means that becoming involved in genealogical research is either easy or unchallenging. The initial state of the system, when we begin our research, contains few members of the system, i.e. we know very little about our ancestors. Historical research can involve a huge amount of time and effort due to the lack of availability of records and the difficulty of either finding them or accessing them. The acquisition of the knowledge and skills necessary to adequately do historical research can be overwhelming.
Contrary to the evaluation of the lady with the challenging ancestral family, those relationships do not involve a significant increase in the overall complexity of her ancestry. In fact, she already seemed to know how the various people were related. Her evaluation was most likely based on a lack of enthusiasm for pursuing the research necessary to document the system, not the complexity of the system itself.