Do such backups retain Signal message history - unlike Apple's native local backups to MacOS?

This uses the same protocol as macOS, so same outcome. However (not sure if it helps in this case), keep in mind that different data is retained depending on whether the backup is encrypted or not (the tool supports encrypted backups too). So maybe check with encryption enabled and see if it carries over Signal messages?

It doesn't. Signal opts its data out of even encrypted local iPhone backups.