The population certainly swells in the summer months as many, many vacationers flock to Hilton Head. I personally know a resident who does go north in the summer months to s second home. I'm not sure what the percentage of people who split time between homes in the summer and winter months, but I'm sure there is a fair number who do. Hilton Head Island is fairly affluent, so there would be people with the means to do so.
However, HHI is fairly temperate, so I doubt you would have as many who travel north in the summer as you may find in Florida. It's more pleasant year-round than places to the north or south. I'd be curious to hear other opinions.
What is the business you are considering?