For sure - but those would not be questions addressed by evolutionary cognitive archaeology (well... not by anyone I would endorse!). We are not looking for the content of the thought (surely lost, unless written down) but its limitations and ability... ie not what someone called something, but did they use language, and of what structure. Not what something symbolised, but if it was indeed symbolic, etc.
Season 1 did contribute to archaeology, data was being recorded and observations made... stay tuned for future papers (not on cognition mind, but experimental, from shelter efficiency to human biomechanics - we're in the writing process!).