On a long timescale, yes, they will. On a short timescale, many people will die. You can't just move an entire house to a different city (and obviously no-one will be able to sell a house on a drowning coastline).

For example, the Pacific Islands will face rising tides along their whole coastline, while simultaneously facing extreme weather events and agricultural disruption. What's your solution for an entire country of people simultaneously trying to immigrate elsewhere?