I know that the umlaut vowels were also written as ae oe and ue, and this orthography shows the process of assimilation with a high vowel. But were these vowels ever actually pronounced as a diphthong, before they became fronted? For example schön being pronounced as schoen, with both vowels being pronounced separately as a diphthong? I think there must've been some sort of intermediate stage of pronunciation between Old High German sconi and Modern German schön.
Umlaut itself—as in the process, not the dots—was a sort of vowel harmony that was productive for a long time in Germanic. The thing you're asking about specifically is called i-umlaut; there was also a-umlaut and u-umlaut.
The way it's generally understood (in Proto-Germanic), when there was a back vowel in one syllable, and an
*/j/ in the next syllable, the back vowel shifted forward in the mouth. Phonetically, this is quite reasonable: these sorts of harmony processes (where vowels shift forward or back to match the syllables around them) are common, and you also see them in e.g. modern Turkish and Finnish.
The back vowels in Proto-Germanic were
*/a o u/, which would have had front allophones
*[æ ø y]. In the earliest written records, this allophony isn't written: it was fully predictable from the context, and
*[æ ø y] didn't show up anywhere else, so there was no ambiguity. The front allophones were used if
*/i j/ were in the next syllable, the back allophones otherwise. Nice and straightforward.
But then, sound changes happened, and certain suffixes started disappearing. For example, the plural of *mann "man" used to be *manniz, with a nice predictable
[æ]. But when that suffix disappeared, the early Germanics were left with *mann and *mænn. The umlaut had become phonemic.
So now, how to write this? The Latin alphabet didn't have letters for these sounds! So different languages improvised in different ways. Old English used æ, oe, y for
/æ ø y/. The Germans used ae, oe, ue, which developed into ä, ö, ü through abbreviation. In Norway, they used æ, ø, y. But by comparing the developments in different languages, it seems clear that these all represented the same phonemes, and that they were monophthongs, not diphthongs.
(P.S. English ended up losing all these fronted vowels, merging them into other phonemes. You can see some of their descendants in man~men, foot~feet, mouse~mice. There was also a vowel length distinction that I'm ignoring here for simplicity: for full details, Wikipedia has a nice chart.)
(P.P.S. Old English was originally written in the Futhorc alphabet, which did have specific runes for
/æ ø y/. But then the Latin alphabet took over, so they had to make do with ligatures and digraphs.)
The answer to your question is no. The German umlauted vowels were never diphthongs. In early New High German they were written as a, o, and u with a small superscript e. Later, this “e” was reduced to two dots. The spellings with ae, oe, and ue are merely typographical attempts to deal with the miniature “e”.