It looks like the answer is yes it is safe after it drys,
Do not expose cats to wet permethrin as it affects their central nervous system. This is not true with dogs, horses, or cows. Cats can be around permethrin treated fabrics once the application has dried.
If a product containing permethrin is applied to a dog and there are cats in the household extra care and caution should be taken to ensure that the cats do not come into contact with the product. The best advice is to apply the product in the evening, separate the dog from the cats, and allow the product to dry over night. Once the product has dried it is no longer a danger to cats or children.
Before spraying any foliage, flowers, fruits or vegetables in your yard with permethrin, bring cats inside and close the windows to the rooms where they are. Speak with your neighbors to let them know when and where you'll be spraying the permethrin so they can keep their cats indoors as well. Keep cats out of the area by covering sprayed plants with garden netting. You can remove the netting once the spray dries, usually overnight, so don't worry about the netting being a permanent fixture. Once the leaves of the plants are dry, it's safe for kitties to come out again.
For households with dogs and cats, either use spot-on products that do not contain permethrin to avoid accidental exposure, or keep the pets apart until the dog’s treatment has dried. This prevents mutual grooming or even the pets sleeping next to each other, which could result in poisoning if your cat became exposed.
Keep your cat separate from any dogs that have been treated for 12-24 hours. This allows the product to dry thoroughly. When in doubt, a t-shirt can be applied to your dog to prevent accidental exposure to your cat until the product is dried.
Keep your cat away from any areas (indoors and out) that have been treated with a pyrethrin or pyrethroid product until it has completely dried.
Pyrethrin/Pyrethroid Poisoning in Cats