Urine contains, as Silurus explained, urea, which is an organic binding of carbon and ammonia. If it were to break down into ammonia, it will work to help cycle the tank, but there are bacteria necessary for that breakdown, and I don't think those would be present, generally, in an uncycled tank in the first place. But if you constantly added urine to the tank, you'd obviously build up some of those bacteria and eventually convert it to nitrate - not that there's any benefit in having more nitrate in the tank, but it would be "food" for the "good bacteria" that live in your tank...
So, I agree with Silurus, it serves no purpose during the cycling of the tank (assuming there is actually some other form of ammonia source in the tank) and would just increase the amount of nitrate (and other waste products) in the tank when it's cycled.
If you really want to convert urine to ammonia, it would be best (and smelliest) to collect it in a container and leave it in a cool dark place for "a while" - not long enough to dry it out, but until it's had access to suitable bacteria.
Whilst on the subject, I just remembered that when they test for urinary tract infection, they look for nitrite. It wouldn't surprise me if it's a similar strain of bacteria producing nitrite from urine as the ones producing nitrite from ammonia in fish-tanks. Not suggesting that you wee in the an un-cycled tank if you have a urinary infection tho'
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Mats