Yes, its safety used as a food additive has been approved by the U.S. Food and Drug Administration (FDA), European Food Safety Authority (EFSA),  Joint FAO/WHO Expert Committee on Food Additives (JECFA), as well as other authorities.

FDA
Sodium carboxymethylcellulose is generally recognized as safe (GRAS) when used in accordance with good manufacturing practice in food for human consumption. (4)

It can be used for anticaking agent or free-flow agent, drying agent, emulsifier or emulsifier salt, formulation aid, humectant, stabilizer or thickener and texturizer in Cheeses, Food Dress, Art Sw Jelly & Fruit Jams and Froz Desserts. (5) (6)

EFSA
Sodium carboxy methyl cellulose (E466) is listed in Commission Regulation (EU) No 231/2012 as an authorised food additive and categorized as “additives other than colours and sweeteners” (7)

Safety re-evaluation in 2017
After the studies of short and long-term toxicity, carcinogenicity, reproductive toxicity and other researches, in 2017, EFSA concluded that “there was no need for a numerical ADI and that there would be no safety concern at the reported uses and use levels for E466.” (8)

http://www.chinafooding.com/Carboxy_Methyl_Cellulose-CMC