No no, Eve is, according to Adam himself, “flesh of my flesh and bone of my bones.” That and the fact that she was taken from his side, not the feet or back which might suggest a lower status, reveals that she was meant to be of equal value to him, not beneath or behind him. They were to tend the garden side by side.
But doesn’t it enhance women’s status to have been created simultaneous with man from the same soil? Go to your bible and read the two different versions.