According to Háčky in this thread, Korean games can migrate Pokémon from any language of Generation III game. This means it is possible to get non-Korean Pokémon (with non-Hangul name and OT) on a Korean game without trading. Korean text entry does allow using only non-Hangul characters anyway, however.
According the UPC, Pokémon that are Korean in origin cannot be traded from a Korean game to a non-Korean game in the Union Room. The sentence about the Classic Ribbon seems to imply that other methods of trading (GTS and Wi-Fi Club) are not prevented from trading Korean Pokémon under these circumstances (although they are no longer available, unfortunately, but there are fan-made workarounds to allow them). Additionally, the wording implies that Korean and non-Korean games can communicate in the Union Room, but Korean language Pokémon cannot be traded to the non-Korean game (so they could still battle, chat, etc. in the Union Room, which should result in the Korean player's name not displaying properly).
Additionally, I've seen several sources describe what happens to Pokémon with Hangul names/OTs in non-Korean games. According to [url=http://Bulbapedia, Hangul names/OTs are displayed as blank spaces in DP, whereas in PtHGSS they show up as dashes. However, other sources (UPC, this GameFAQs user) state that they are rendered as question marks in PtHGSS.
In Generation VI onward (at least), Eggs traded from games of different languages display the name of "Egg" in the Egg's language of origin (for example, I have an Egg named "uf" in my English Y; it remains French in origin when hatched, but I can nickname it). I'm not sure whether this occurs in previous generations. If it does, you might be able to send Korean Eggs to a non-Korean Gen IV game using Spin Trade.
So, my main questions are:
- In what way are Korean and non-Korean Generation IV games incompatible? Which communication features can and can't they use (of all kinds, not just trading)?
- If a Pokémon that legitimately has a Hangul name/OT is (legitimately) traded to a non-Korean Generation IV game, how is it displayed?
- In which games did "Egg" start displaying as the Egg's language of origin? Does this go all the way back to Gen II?