No that’s not the case at all. The body in its quest for homeostasis will automatically over time downregulate receptors that it views as over-activated. This is a super simplified explanation but easy to understand - this is how tolerances of any kind are built up. Over time when you give your body anything in excess - for instance caffeine - your body starts to desensitize receptors for caffeine and you have limited effects.
If androgen receptors were upregulated upon saturation then you would, given that idea, constantly have unlimited androgen receptor upregulation and in fact increased sensitivity over time. You’d never stop growing from androgens - which we know isn’t true.
In its quest to maintain homeostasis the body will always downregulate receptors which are constantly saturated. I believe I posted a video about this idea in the past.
Don’t confuse regulation with sensitivity either. When you take testosterone you add more androgen receptors - but they also become less sensitive. The body is smarter than you. This is actually similar to insulin sensitivity. When you constantly bombard cells with insulin they stop listening - they become LESS sensitive when MORE hormone is present over time. @alldayeveryday