Can sarcoidosis effect testosterone production (hypogonad disease)?

Yes. Hypogonadism appears to be common among males who have sarcoidosis. In a 2007 belgian study, male patients with sarcoidosis had significantly lower median circulating levels of testosterone than healthy age matched controls. The mechanism is thought to be due to testicular dysfunction or disruption of the hormone signals from the pituitary or hypothalamus.
Possible. Sarcoidosis does not typically cause this but if is possible if the disease affects this pathway.