I just did this a month ago. Bought a 4-leg itinerary from LH, last leg a code share on UA metal. Easily applied a GPU on UA.com, where I sat on the wait list for 2 weeks.

However, when I checked in for my 3rd LH leg it auto-checked me in for the 4th (UA) leg. Unfortunately that knocked me off of the UA upgrade wait list. I got back on the morning of the flight by manual intervention on the part of the UA TA in FRA (and got the upgrade!). However, this appears to be a common problem.

I know from experience you will not lose the upgrade if it cleared before check-in, and it usually isn't a problem if you can check in for the code share on UA.com. Just be aware that certain situations can be a problem.