Yes, he will most likely have to wear a monitor. Passive house arrest (no monitor) is extremely rare. Are you asking about counties in South Carolina that do not require monitors? You may want to talk to the attorney who handled the matter.
Being on House arrest doesn't necessarily mean that he will be on an electronic or GPS monitoring system. You need to look at the bond order and see what it says. Generally, if a monitor is required, the Judge will state that GPS or electronic monitoring is required in the bond order. The individual counties have nothing to do with whether he has the monitor or not. That will be solely up to the bond judge and will apply in whatever county he goes to for his house arrest. Keep in mind too that generally when someone is on house arrest they have to provide an address to the court, so he's not going to be able to go from location to location without further court approval.
This answer is intended for general information only and does not create an attorney-client relationship. You should consult with an attorney for detailed information as each situation may be different. Do not rely on the information given in this answer, and proceed at your own risk should you decide not to consult with a state licensed attorney first.