Will the new iPad (bought in Korea) work in the USA?
Yep, it will work in the USA. There is no difference in the hardware for a cellular iPad bought in USA or in any other country. 

All iPads have been sold unlocked since their release. So yes, it will be unlocked.

Source: http://store.apple.com/us/question/answers/ipad?tqid=Q79JKFTAAKPHKF2FTPT47A24U4YAUH79K


  "Both the AT&amp;T and Verizon model of iPad can roam worldwide on GSM/UMTS networks. In countries without compatible 4G LTE networks, the new iPad will operate on GSM network technologies such as HSPA+ and DC-HSDPA. 
  When you travel internationally, you can use a micro-SIM card from a local carrier."