There is no clear way to search for upgrade availability.
If you purchase a Y or B fare ( and in some cases M), you can request the UG
through Mileage Plus only. There is no assurance that you will get it.

Further, I believe there is no wait list for these UG's. Even if it is refused, space
may come open later,and you would have to put in a new request.

It is usually cheaper to purchase a Z fare than a Y fare.