If it's non-revenue and the crew agrees why can't you get approval?
Don't they do test flights with an engine out on takeoff?
They do flight tests where they do a fuel cut at V1, but I've never heard of a test where they did a takeoff on a single engine from brake release. And there are special requirements for such tests - including doing it out of some place like Edwards where if things go badly they're not apt to land on someone... (although to be fair, there's not much around Iqaluit to hit if it does go wrong)
The FAA tends to frown on such things - even for flight testing or non-revenue.