"Charged cotton" has 5% elastane for stretch. So, yes, cotton with synthetics in is an apt description.
However, in broader terms, I am not convinced of natural fibers produced via modern agriculture being significantly more eco friendly than synthetics.
A cursory glance at emissions - although data does vary depending on source - doesn't really support the idea of cotton being particularly clean in contrast to, say, lycra.
There are probably other differences because synthetics aren't biodegradable, but knowing modern agriculture and it's enthusiastic use of fertiliser which ends up in water... i couldn't make a definite statement which is worse.
I'm just find the automatic assumption that natural being somehow better or desirable on it's own to be fallacious. If it has better properties for what you're trying to do, sure - while I don't very much "dig" merino base layers, my go-to winter socks and cycling cap are merino, but avoiding synthetics elsewhere just to avoid synthetics - meh.