Not worth it
I tried, and after spending considerable efforts eventually scrapped the idea.
I expected magazine problems others referred to, but magazines worked fine. One issue was that cuts in barrel extension that let bolt lugs through have the same width for 5.56 and 7.62x39, but the latter has larger bullet. Because of that 7.62x39 bullet tend to get stuck on the ramp when corners of barrel extension dig into it. Only happens once in 100 rounds or so.
The other potential problem is that 7.62x39 casing is tapered so its bottom area is larger. This has two implications. First, bolt thrust is higher, even though 7.62x39 is a lower pressure cartridge than 5.56. Second, there's less metal left in the bolt to support the lugs. These two effects combined can cause bolt lugs next to extractor to crack much earlier than lugs of 5.56 bolt would.