The ability to use colloquial, formal and academic speech/writing is a very good indicator of proficiency in a language.

yes, using of formal english will tell people how good or proficient you are in English.

From what I remember from high school english at RV, many of the words in english that are often thought of as being more, maybe specifically descriptive or academic are actually words imported from french and latin. There was two different time during which this occured; the french words were brought into the language after the Norman conquest of 1066 and the latin words during the renaissance when there was an increased interest in classical civilization. I forget the name of my high school english teacher but can remember her face, sort of.

In my humble opinion, it is not necessarily the case. For a learner that does not speak English at all, studying formal expressions is no more difficult than spoken, informal and slangy ones. In fact, there was a time when I wrote and spoke with only formal lexicons. I met a Chinese learner that only knows some classical Chinese, and has serious difficulty in making himself understood, and knows very little about everyday communication phrases and grammar. Hence, I believe that using formal words is merely a style. It has nothing to do with proficiency. I think that those who speak and write with multiple styles in different situations appropriately and clearly are true advanced speakers. I personally think that for most learners, intelligibility, clarity, accuracy, appropriateness, and the ability to address a greater number of topics are of more substantial significance and higher priority than style because the majority of us, non-native speakers, do not work as editors, linguistic researchers or authors in this foreign language. Nevertheless, if a learner has a formal style, they appear to be wise to native speakers since the latter use informal spoken English more frequently.