It should, due to lower aromatase levels in the lower body fat condition. Aromatase converts testosterone to estrogen. The body tries to maintain a certain estrogen level. If estrogen starts to drop due to less body fat and aromatase enzyme, the body will increase testosterone to try get estrogen back up, ie trying to compensate. Also high estrogen is suppressive to the HTPA.
If body fat levels get too low, testosterone will also lower. This is mainly due to the low calories/diet required to get to low body fat levels supressing hormone levels.