There are various considerations here. If this person has been on exogenous testosterone for a long time then a single, short-lived crash of estradiol is not going to be enough for an HPTA restart. If the AI dosing were continued indefinitely and if the exogenous testosterone doses were low enough then it is possible that some HPTA activity would be restored. It's complicated because both androgens and estrogens apply negative feedback to the hypothalamus, suppressing the production of GnRH. AI use can wipe out the estrogens, but the androgens may still keep things from working if levels are sufficient. At the pituitary only estrogens are suppressive. Therefore, if the pituitary receives GnRH and estrogen is low—or blocked with a SERM—then LH will be produced after a startup delay.