Chase Ultimate Rewards points can be converted to United miles. See information about United's upgrade options here:
https://www.united.com/web/en-US/con...t-02-01-14.pdf
I am not a UA flyer, but it appears that an upgrade from discounted economy requires 20,000 miles plus $550 one-way (40,000 miles & $1100 round trip), in addition to the cost of the paid ticket.
One way business class tickets can be had for 25k miles + $5 if booked far enough in advance. That sounds like a much better option than upgrading a ticket.