Does it ? For what I know, in Chinese and in Japanese, kanji compound are read left to right, that is a kanji (or group of kanji) on the left are usually qualifying what’s on the right. So it can be argued that the most important kanji is often the last one, well at least it tells us what the word is about.
Like for example 海水浴. 浴 is the last one, so we are talking about a bathing. What kind of bathing ? In Water. What kind of water ? Water from the ocean. (so the word mean ocean bathing or seawater bathing) Which kanji has the stronger weight ? I’m not sure… Same in English, what is the most important part of “seawater bathing” ? Is there really one ?
Unfortunately, none of it probably matter in the very specific case of 会社/社会, because the etymology seems very messy.
From what I understand, the modern meaning of both words were created in japan, as a single translation of the word “society” (from dutch and english). Seems that for quite a long time 「会社」「社会」「仲間」「連中」were used in a similar way, to talk about a small community (like club or small company) and it’s only at the beginning of Meiji era that the meaning of 会社 and 社会 clearly diverged.