I'd say it's a pretty sure thing - if you see award availability (U), then chances are it will clear with an upgrade voucher. Even when there is no award availability upgrade vouchers have a better success rate in my experience compared, say, to avios upgrade requests.
For me personally, the process has always been the conventional one via email (hence there can be an anxious wait, hoping someone else does not beat you to it), however as the previous poster mentioned - some concierge agents can be particularly resourceful over the phone.