Beyond idiomatic yojijukugo (or perhaps because of it?), 4 mora abbreviations seems to be really common in Japanese. E.g. "debadora" for "device driver" [1]
They are indeed. I participated in phonology seminar in Tokyo U years back, and it was very interesting. According to the prof, Japanese phonology definitely has a tendency to use "moraic foots", that is, units of two mora, as a preferred unit of morphophonologic processes, which then maps to abbreviations of two-word phrases where each of the words get their own foot: deba-dora.
I'd say that yojijukugo are not necessarily directly related, as the readings of the kanji can be one or two mora, so there's some variability in the structure of the readings of yojijukugo.
That being said, people often say that because of moras and foots, syllables have no place in Japanese phonology, but that's not true. Japanese pitch accent patterns (of Tokyo Japanese) depend on the syllabic structure.
Just to make it clear, this doesn't only apply to imported words (although it's probably where it's more common). It works for purely Japanese words too. For example: なるはや (naruhaya) is a 4 mora abbreviation of なるべく早く (narubeku hayaku). Another one: あけおめ (akeome) is an abbreviation of 明けましておめでとうございます (akemashite omedetougozaimasu)
[1] https://news.ycombinator.com/item?id=23798995