Either way should be packed, as the Conrad is in a major office area.
My perception is that the fairly laid back Seoul subway commuters would be less annoyed than those in Tokyo by foreigners with suitcases, especially if originating from GMP or Seoul station.
Inbound traffic from Incheon is very dense in the morning as well, although the Conrad benefits from being closer to Incheon than most hotels (traffic starts backing up shortly before it).