Does `--no-atomic` guarantees to update refs before the one with an error?

The flag --atomic for git push guarantees that if the command either succeeds or no refs are updated.

Does --no-atomic just turns off this guarantee or does it establish the opposite guarantee - that all the possible references will be updated even if there are some errors (or at least that the refs before the incorrect one will be)?

For example, if I run the command git push --no-atomic origin foo bar, will foo be updated on remote even if there is a problem with bar?

git push --no-atomic reverts to the default behavior, which is:

• update as many refs as possible and
• report errors for all refs that could not be updated.

In your example foo would be updated even if there is a problem with bar.