Just because it is synthetic does not necessarily make it better for your application. The additive packages in engine oil and transmission oil are very different. Engine oil is good at anti-foam and controlling acids. Transmission oils are good at handling small amounts of water, have anti-friction additives for high power gears, are wet-clutch friendly, and work well in medium pressure hydraulic systems.
Will it work? Maybe. It depends on what tractor you have, which you didn't mention. But if it were my tractor I wouldn't use engine oil in the trans unless it only had a manual transmission, dry clutch, and no PTO clutch. The perceived "improvement" in oil life is not worth the risk of replacing a burnt clutch. And depending on the age of the tractor there is a small chance that you might induce oil leaks due to different amounts of swell in the seal material.
ISZ