In short, the answer is yes. 女 is a semantic component women.
We haven't found this glyph in oracle bone script or bronze inscriptions; the earliest is in the Small Seal Script. It was originally written as 媆. It's both ideogrammic and phono-semantic. The semantic components are 女、耎, and 耎 gives the sound. 耎 is again both ideogrammic and phono-semantic. The semantic components are 而、大, and 而 gives the sound.
As semantic components, in general, 女 refers to women, 而 refers to beard, and 大 refers to person/human. 耎 means 0) with very very long beard. It's extended to mean 1) front-end slightly larger than the other end and 2) tender. However, meanings 0) and 1) are rarely used. Meaning 2) is also written as 媆, which strengthens the meaning with women, who are characterized as tender.
媆, writing as 女而大 and undergoing some catachresis (訛變), finally became 嫩.