Taxing Matters
Overtaxed Member
Umlauts are used in the English language. One word that comes to mind is naïve (although naive, without the umlaut, is also used).
I think it's more accurate to say that umlauts appear in foreign words that English has incorporated. They are not part of words that originated in English nor part of our English alphabet. In formal terms, they are not part of English language construction. They appear only because we incorporate some foreign words that do use them, and even then most of the time when people do use them they do so without the accent.