Good question. Since the amendment of the ESA in 1978, I believe there have only been six applications for exemption from the ESA made to the Endangered Species Act Committee (God Squad). Three were withdrawn, one was denied (Tellico Dam, TN), and two were granted (BLM Timber Sale, OR and Grayrocks Dam, WY and NE). The exemption for BLM timber sales in OR was later withdrawn.

Not much history to go on to figure out exactly how the system would work, and there has been a long time since the last action under this exemption process, close to 30 years I think.

Here is a good link describing the past exemption requests made:

ESA Exemption Applications - Congressional Research Service

Legal review of the exemption process, Notre Dame Law Review:

How the God Squad Works