You may or may not run into complications if you try to request a price adjustment while also preserving an upgrade after having applied a GGU (or I suppose been instantly upgraded if your elite status, fare class booked, and U space availability permitted it). I've done this over the phone many times in the past without issue, but my recent attempts have required playing HUCA. One example: https://www.flyertalk.com/forum/36467500-post773.html

So if you do see yourself in this situation, I think you should still be able to call in and secure the price adjustment while still preserving your upgrade. But as mentioned, you may have to play HUCA for a bit.