You can rely on Time Machine to backup your protected folders, but this is generally discouraged for two reasons:
That said Time Machine can be used with Espionage, but is encouraged as a supplement to Espionage's convenient and efficient backups. Time Machine will automatically backup your folders, and is on Espionage's white list by default so its operation will not bring up the password prompt.
One note to keep in mind is that by default, Time Machine will not backup your data in an unencrypted state (unless you are using unencrypted, password protected folders), even while your folders are unlocked.