I would love it if someone who knows more about this than I do would confirm/deny since this is something I've been curious about for a long time now. (Though I would also love a tool for near-lossless cutting that just re-encodes the cut GOP, please link such a thing if it exists)
Yes, but then you'd have to render the result into a truly uncompressed format and it would have to stay in that format perpetually. If you wanted to deliver in another lossy format, you'd actually lose quality across the entire file instead of just the one GOP.
What I'm curious about is whether you can cut in the middle of GOPs, recompress the afflicted ones, and then concatenate the stream back together without recompressing all GOPs. If the file specifies a 12-frame GOP, cutting any GOPs is going to break that cadence. So can you have, say, a few thousand 12-frame GOPs... then an 8-frame GOP... then go back to 12-frame GOPs?
Update: Did some research and you can have "adaptive" GOPs of varying lengths: https://docs.aws.amazon.com/mediaconvert/latest/ug/gop-struc...