Starting from assumption that Korea may have held the same worldview as philosophers from ancient Greece, India or the Near East, which stand in correlation to the local literary traditions and mythical beliefs of Indoeuropean (e.g. Norse mythology) and Egyptian origin, no, that is not the case.

The common belief in both Goryeo and Joseon was that the earth was just a infinite plane that doesn't end anywhere. As for the heavens, there was no reason to assume the empty space above them just stops at any point, so it just extends infinitely vertically as the place they stand on extends infinitely horizontally. There isn't much further sophistication beyond that and no real alternate models than what people at that time found reasonable (disks, plates and forms with edges seem inherently innatural, observable in nature itself). As to when Koreans (and in general the isolated places of the Far East) found out about the existence of the Americas and that you're able to sail around the Earth is unknown. Likely it was either through Portuguese merchants or Jesuit missionaries Koreans met, when visiting the Qing empire.

As for the egg-shape model and the non-infinite disk with a circular heaven that originated in Chinese philosophical beliefs, they are oftentimes metaphorical and not meant to be taken literally. It didn't bother much, what the Earth actually looked like as that wasn't all too important in Confucianianism. There have been theories about a circular Earth from observations of the moon and how it reflects light as a "silver ball".

As for something tangible, in 1427 the royal astronomer Yi Soon-Ji made the observation that during a solar eclipse the moon threw a shadow onto the Earth and brought up the assumption that at least the moon was a ball (and that Earth wasn't infinite) as well as neither moon, nor sun and earth being fixed objects.