In practice, vote secrecy does not appear to be a priority concern of the authorities. More so when you have to educate more than 3000 local authorities [number of counties in US] to pay attention to the issue. I did a quick duckduckgo for images of US mail-in ballots, and found many instances of mail that have the sender information on, as is customary for US postage. Found even a couple pictures of ballot envelopes from Portland, Oregon, where they explicitly ask the voter to provide a return address, that is to tie their identity to the ballot:

https://imgur.com/ZRHuLWd

http://mediad.publicbroadcasting.net/p/northwestnews/files/s...