i think you mean sex rather than gender and they can't imo.
No, gender is a cultural aspect strongly influenced but not entirely determined by biological sex. Similarly, age is a factual count of the number of revolutions of the Earth about the Sun since an individual's birth, whereas being 'old aged' is a cultural assessment of that age.
You can decide that you don't want to be 'old-aged', or 'elderly' and society will have various opinions about that choice depending on how old you are and how the particular culture you're in views that.
O.