If you should decide to delve into the "cutting edge" archaeology literature of the 1970s and 1980s (and unless you are an archaeologist, I don't recommend that you bother), you will come across a number of different books and papers promising that archaeology can and/or should study any number of things that archaeology is, to date, rather unsuited to studying.
These sorts of claims come in two basic themes, with each of these containing many different flavors. Theme #1 can be summed up by saying "all human activity leaves behind physical traces, and therefore the study of the physical remains of human activity (that is, archaeology) can examine all human behaviors, provided that we can figure out which questions to ask."
This is, at best, an overly-enthusiastic belief. It is not really true, but it may be a useful delusion. It's open to debate whether or not all human activity leaves physical traces behind, and even for those that do, the traces are often not meaningful. For example, a fist-fight would leave physical traces in the scuffling on the dirt, but even if, through some miracle, these mild surface disturbances were preserved for examination by future archaeologists, it's unlikely that it would be determined that this was the result of a fist fight and not any number of other activities.
However, there are plenty of cultural phenomenon that it was long assumed could not be studied archaeologically that archaeologists, armed with the attitude that everything could be studied archaeologically, figured out ways to study. These range from studying prehistoric economics to socio-political organization to general religious cosmology. The degree to which these things could be studied, and the validity of some of the interpretations offered, is highly variable. But, nonetheless, there has been some success, and without the "we can study anything, we just have to figure out which questions to ask" attitude, and poor explanations have frequently been the starting point down the road towards better explanations.
So, it may be useful for us to fool ourselves into thinking that we can study anything through the archaeological record. But just because it's useful doesn't mean that it is true.
The second theme can be summed up as "all human activities are about/partially about X, and therefore we can use the study of material culture to study X." X can be many things: power relations, gender politics, group or individual identity, etc., etc., etc. Again, there may be a good reason for encouraging this behavior - it encourages people to look at how our material culture and the distribution of materials across the landscape may reflect, and allow the study of, these more ethereal aspects of human behavior. However, it is based on a basic fallacy - the notion that all material remains of human behavior are marked by some ephemeral thing (power relations, gender politics, a desire to pour yogurt on all things), and that this ephemeral thing can be examined through a careful study of the material culture*. Even allowing that most of us don't appreciate the degree to which our material culture does reflect the cultural seas in which we live, and therefore something as seemingly innocuous as a box of breakfast cereal can actually tell quite a complicated tale about the culture that created it, it still doesn't follow that every piece of detritus left behind is useful for examining our lot as a culture.
I have always been amused by what I see as the over-reach of my colleagues. Again, I need to say that I do think that this over-reach can be useful as it may push us to find something new rather than write it off. However, it is still over-reach nonetheless.
Whenever I hear that anything and everything is open to study via material culture, I think of the old saying "when your only tool is a hammer, every problem looks like a nail." When studying people long gone, all that we have is their materials culture, and we don't like that there may be things that will always be unknowable. So, we assert that we can study it all, even though we actually can't. It makes us feel better, even if it is false. And even if it is false, it does push us in some interesting directions.
*It should probably be noted that interest in these subjects is most common on what is often referred to as post-processualist or post-modern archaeology. Much of the research in these areas is quite solid, but some of it is performed by people who are very open about being more interested in forwarding a personal or political agenda than in an accurate reconstruction of the past.