I think it is safe to say that he is 'just' an archaeologist. As mentioned before, archaeology is a sub-discipline of anthropology. Broadly speaking anthropology is the holistic study of mankind, while archaeology is the holistic study of mankind through material remains.
It is the 'material remains' addition that really broadens archaeology. Text, such as books or the familiar hieroglyphs all constitute material remains. When these remains (text) are used, the field is narrowed slightly more into Historical Archaeology, which is not defined by location or time, simply by text by or describing a culture. I think Indy was definitely more of a historical archaeologist.
On the subject of language for the archaeologist, I find that it is rather silly for a general archaeologist to know (to the extent to be considered and expert) an ancient language. In Germany, I have worked with those of the "Old School" who studied Latin and Greek that was forced upon them when studying archaeology. Great, good for them. BUT, it never helped them in the field, that is to say excavating in Germany! Latin did come up when we excavated Queen Editha from Magdeburg, however, the translation of the text was confirmed by experts even though the chief could read it. It always is better in reports when you have an expert opinion if you do not have a speciality in that field.
I am at the post-graduate level of archaeology and have excavated around the world, but I have yet to find one language that would have been useful on every dig (with regards to interpreting the past). However, I do have an expertise on human remains, specifically human osteology (bones). I have excavated thousands of them and found that from a majority of them you can essentially "read" a history of that person. This history, generally known as a osteobiography, can tell age, sex, stature, ancestry, occupation, and pathologies. From a single site with enough human remains you can create a rather detailed palaeodemography of past society. This skill of "reading" bones is one of the few that can be applied to every (minus a few exceptions where human remains have not been discovered for a culture) archaeological society. Some would say I am an archaeologist, physical anthropologist and osteologist. I would disagree. I am just an archaeologist with a specialized set of skills.
An archaeologist must also understand the history and culture of a past society. Sometimes that includes studying modern 'primitive' societies to apply cultural model on past societies. The archaeologist who does this does not transform or change fields to an ethnologist or cultural anthropologist. They apply theories, methods and models, of these fields TO archaeology, just as I apply physical and forensic anthropology TO archaeology. It does no good to be pigeonholed in science. You must build on what others have done and if it relates to your field, use it! I have had to take medical courses and read journals meant for dentists because I can use their expertise for archaeology.
Knowledge of ancient cultures and myths applies a lot to burials. For example, are they buried with grave goods? Are they facing the East? Fetal position? Sacrificed? Were there skeletal modifications for beauty (foot binding, etc) or for social status (removal of the frontal incisors, West Africa)? Without knowledge of these cultural traditions and mythologies, I would be at a loss as to one would bind their infants forehead or purposefully cripple themselves. Before going to a site, I make sure I know the culture, know the site, the mythology, the history, and the medical practices.
On a personal note, I was upset with the transformation of Indy (in terms of linguistics) from Raiders to Present. Look at Raiders from an objective point of view and see if you get the impression he studied linguistics. Doesn't speak Hovitos, doesn't know the writing on the Headpiece, knows only a LITTLE German it would seem (the man asking for water at Tanis, Indy looks a little confused; but when approached at the submarine bay he knows to comb his hair). Come on, there is no reason Belloque could have learned Hovitos and Indy couldn't. I think the whole language thing (from books, Young Indy, etc) really differs from the Raiders Indy, although I do believe language is an important tool.
I hope this clears up my general point that archaeology is a multifaceted field that borrows from many disciplines, but I contend that it is still 'just' archaeology, just as Indy is just an archaeologist.