It is claimed they did manage to evacuate about 1 million Jews (my SOs grandfather was one of them), but no decent citations exist that I've been able to find and more academic sources are skeptical. There were something like 16 million people evacuated in 1941 and several million more in 1942, so it is likely quite a few were Jewish, though given how disorganized it all was there is simply no way to tell or what happened to the people specifically once they were tossed where ever the trains took them. As it is the range of Jews killed in WW2 within the 1941 borders is between 700,000 to 3 million, because there simply is not a way to tell what became of millions of people; they might have survived, they might have died in the Holocaust, they might have died incidentally during or after the war. Confusion reigned supreme and Stalin wouldn't allow a census, so the first one that happened after the war happened in 1956 after Stalin's death as he wanted to cover up the immense casualties that were caused by his failures. That of course wouldn't be the first time he did that when he 'corrected' the 1937 census when it showed just how many died as a result of his policies in the 1930s.
This paper talks about the issue:
Abstract. Previously unknown data from central Russian archives show that Soviet, post-Soviet, and Western historians have substantially overestimated the
academic.oup.com
For any such deportations to happen they'd have to plan ahead to evacuate vulnerable and useful people from the zones in front of the defensive lines.