Do people do it? Yes, but the margin of error off cycle is much lower because you can’t build your hormones up as fast with hpta suppression and no exogenous hormones.
Inhibition of estrogen can lead to an increase in testosterone, which can definitely be good for recovery, but unless you were tracking your blood work constantly, I don’t think the benefits outweigh the risks. You could end up depriving yourself of even more hormones. YMMV based on your biology though.