Yes, its safety when 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
It can be used as an antimicrobial agent, antioxidant, color or coloring adjunct, dough strengthener, flour treating agent, oxidizing or reducing agent, processing aid, surface-finishing agent. (2)

EFSA
Sodium erythorbate (E 316) is listed in Commission Regulation (EU) No 231/2012 as an authorised food additive in the EU as “Additives other than colours and sweeteners”. (3)

Safety Re-evaluation in 2016
After the studies of genotoxicity and carcinogenicity and others, EFSA claimed “there is no reason to revise the current ADI of 6 mg/kg bw/day and the use of erythorbic acid (E 315) and sodium erythorbate (E 316) as food additives at the permitted or reported use and use levels would not be of safety concern.” (4)

Authorised Uses
The following are the approved uses and max usage, which are the same with that of erythorbic acid. (5):

http://www.chinafooding.com/Sodium_Erythorbate