It depends on whether you define the FSH/inhibin feedback loop as part or sub-part of the HPTA. If not then you may be able to say that exogenous FSH does not suppress the HPTA. It may reduce endogenous FSH, however. Wikipedia says "In males, FSH induces Sertoli cells to secrete androgen-binding proteins (ABPs), regulated by inhibin's negative feedback mechanism on the anterior pituitary. Specifically, activation of Sertoli cells by FSH sustains spermatogenesis and stimulates inhibin B secretion."
There's some additional complication, in that if you drive up inhibin it could end up "competing with activin for binding to activin receptors and/or binding to inhibin-specific receptors." The potential problem with that is that activin "participates in androgen synthesis enhancing LH action in the ovary and testis. In the male, activin enhances spermatogenesis."
Given all this it's not exactly clear what will happen to an eugonadal man who takes FSH.