There is still some dispute over some of the related issues. I know some linguists who separate SWH from "Linguistic relativity." It is clear that there are ideas we can have without necessarily having the language to express them, but similarly, in groups with fluent polyglots the language in use shifts regularly according to the subject/topic. It seems clear that polyglots will prefer one language over another, and that seems to be correlated with the subject, but research in this subject is hard, and clear, unambiguous and uncontroversial results are rare.
A single word can hold a large amount of meaning, but to the brain that single word uses the same "storage" and any other word.
So by having many complex words a person can think more "efficiently".
This is why many fields have jargon - the jargon helps the thinking process, by essentially acting like file compression - you compress an entire concept into a single word, and you can now think about some big complicated thing by using a single word.
This is also why language have so MANY words. English has something like half a million of them. Yet it would be totally possible to replace the vast majority of them with simpler, but more, words.
But doing so has drawbacks to thinking ability.
http://en.tokipona.org/wiki/What_is_Toki_Pona%3F
When you see a bug, you a bug, whether it's a cockroach or a spider. Thinking becomes clearer and simpler (or so they say).