Verified answer

The special character "ë" will only appear in the passport if the country of issue uses this special character. A friend of mine named Jürgen Kürten has emigrated to the United States. In his U.S. passport his name is shown as Juergen Kuerten.

You'll find out when you get it back :-)

But an umlaut on an E is easy to do on a computer, which is what they obviously use to create the passports. Plenty of non-English languages using the Roman alphabet make extensive use of accented characters, so I would be utterly gob-smacked if the passport service fails on this.