The storm, which had a peak wind gust of 106 mph, swept into the 520,000-acre preserve that straddles the Tennessee-North Carolina border on Monday evening.
In southeast Texas, the storm was blamed for severe flooding that killed at least five people, while it damaged hundreds of homes and forced schools to close in northern Louisiana.
Louisiana Gov. Kathleen Blanco on Tuesday declared a state of emergency for 11 parishes, and ordered state emergency management officials to send teams to assess damage. FEMA pledged to send teams later this week, authorities said.
One of the hardest-hit areas was Grayson, a town in north-central Louisiana's Caldwell Parish, which received 17 inches of rain between Sunday evening and Tuesday morning, the National Weather Service said.
In parts of northern Louisiana, the totals were the most in a single storm event since the Tropical Storm Allison in 1989, the agency said.
"The rainfall amounts were exceptional," said meteorologist Nick Fillo. "Outside of a tropical system, it happens every once in a while."
In the Great Smoky Mountains National Park in Gatlinburg, two people were injured, including a 6-year-old boy when a tree fell on his family's camper, authorities said.
The storm came during one of the park's busiest seasons as thousands of visitors travel there to see the brilliant fall foliage.
"We are not evacuating, but we are advising campers to vacate at least through 8 a.m. (Wednesday)," park spokeswoman Nancy Gray said.
Major roads closed for debris removal included a road that links the Tennessee and North Carolina sides of the park. Officials hoped to have the road re-opened Wednesday.
In Texas, floodwaters from the San Jacinto River seeped into subdivisions in Houston's northern suburbs Tuesday, a day after torrential storms and tornadoes wreaked havoc. An 18-year-old man who drowned when his horse got scared and threw him into the water was among the deaths attributed to the storm.
The National Weather Service issued a flood warning for the West Fork San Jacinto River until late afternoon Thursday, as residents of stilt houses hauled belongings out of their sheds and yards while those in ground level houses moved to motels to avoid the rising water.
"Just because the rain has stopped does not mean the flood dangers have ceased," said Gloria Roemer, spokeswoman for the Harris County Office of Emergency Services. About 50-250 households could be affected, Roemer said.