There are two LaRoche houses in old Savanah -- the one you mention and one called the E.M. LaRoche house (now a duplex) on Tattanal
That house was built by Augustus LaRoche a brother to Issac Drayton LaRoche. These and several others were merchants inm Savannah -- successful until the War between the States.
The brothers descend from Issac LaRoche a merchant from the Augusta Area. This Issac was the son of the first Savannah LaRoche as described below. This Savannah LaRoche family is not directly related to the first South Carolina imigrants (circa 1690).
If you will check the Georgia Charter and the original governing board documents (circa 1732)you will find the mention of two LaRoche names. John was an MP and his brother was a merchant. They had a third brother who was a merchant in Bristol.
Their father was the Minister of the Bed Chamber for George the Prince of Denmark who was Queen Anne's husband. She died childless by him and so the Crown by act of Parliemnt went to the House of Hannover. Lady Churchill was the Lady of the Bed Chamber for Queen Anne.
Peter Crothaire (derivation of de la Croix), a Huguenot of the Bordeaux region (his parents were bÃ©arnais, from the region of BÃ©arn near Navarre), changed his last name to LaRoche (upon marriage?), during his service to the husband of Queen Anne. BÃ©arn was a small semi-independent province, immediately north of the PyrÃ©nÃ©es, about 45 miles long and 35 miles wide. Pau, its capital, lies at the center. It formed a considerable portion of the Kingdom of Navarre. Today Pau is included in the Department of Basses PyrÃ©nÃ©es.
As noted above, one of the Trustees of Georgia at its founding, John LaRoche, descended from Peter Crothaire nÃ©e LaRoche(see also http://www.cviog.uga.edu/Projects/gainfo/tdgh-nov/nov10.htm
Isaac LaRoche, was born in Savannah. He became a merchant-farmer in Richmond County, Georgia. Records indicate that his father was a soldier in the American Revolution.
It was this LaRoche (Issac's father -- who was also named Issac) who was related to the
three English LaRoche's previously mentioned. I believe he was the son of the Bristol merchant, but I can not prove it.
Isaac's wife, Elizabeth, was the daughter of another "American" soldier from London, who allegedly provisioned his fighting company out of his own pocket after immigrating to the Augusta area.
She was also the granddaughter of Donald MacKay, who as a child first settled at New Inverness (Darien Ga.) in about 1736. Donald's Scottish father was killed or captured at the battle of Moosa (1740) when Donald was only nine. Donald overcame this tragedy and later owned part of St. Simons Island, including possession of Fort Fredricka, after the Spanish were no longer a threat to English holdings in Georgia. The abandoned tabby (shell concrete) buildings at Fredricka were recycled because of a lack of materials at the time, leaving only the base outlines tourists see today.
Hope this helps with background, sorry I have nothing on I. D. LaRoche directly