Does the use of お instead of う to lengthen a vowel have any effect on pronunciation?
I’m also curious about what constitutes the “right” spelling here given that it is normal to use kanji anyway. For example, when would I write or encounter こおり instead of 氷 outside of beginner/children’s books? Will I occasionally see コオリ for emphasis? Or what about コーリ? If I write こうり how wrong or incomprehensible is that?
No, but it’s essentially a result of etymology. Long Os formed with お are generally kun’yomi readings, while う are on’yomi. (I don’t want to say “always”, because the golden rule of Japanese is “all rules have exceptions, including this one”, but I’m pretty sure it’s always.)
Any time you need to type it. You average IME is not going to suggest 氷 if you type こうり, unless it’s got some kinda telepathic autocorrect equipped.
I wanted to follow up with a photo of a shaved ice stand at a festival for a situation where you might see the kana in the wild, but those are generally written かき氷, so perhaps not the best example.
コオリガモ is a species of duck (Clangula hyemalis), so possibly, depending on how interested you are by ducks, since animal and plant species are frequently written in katakana.
Almost certainly not, though I wouldn’t put it past some writer trying to be clever.
People are probably gonna go “Did you forget the つ while you were typing 効率?”
You’ve also picked a slightly less day-to-day applicable example to talk about - 通り might see greater amounts of regular usage.
Obviously “enjambing” two on’yomi which start / end with an “o” sound is not quite what is meant in this thread, but examples like 保温 exist of words which read using on’yomi and have “oo”.
In kun’yomi land, I learned that Hagrid in the Japanese translation of Harry Potter is described as an 大男, which is kind of awesome.
Indeed not, but I knew someone would be along sooner or later. 
Then there’s the JR 青梅線, an offshoot of the Chuo Main Line in western Tokyo, which is kun’yomi (albeit slightly abbreviated from あおうめ), and, just to be confusing, is typically written in romaji as Ōme.
There’s also an
From what I understand, the お vs. う distinction doesn’t affect modern pronunciation at all. Both produce the same long お vowel in speech. The reason certain words like こおり and とおる use お rather than う to extend the vowel is historical as those words had an older phonological origin that got preserved in the spelling, but a modern Japanese speaker pronounces them identically to how they’d pronounce a word spelled with うう or おう in that position. So you’re not going to hear a phonetic difference even if a native speaker is aware of the spelling distinction.
As for こうり, it’s wrong, but not incomprehensible. A native reader would understand exactly what you meant and would also immediately clock it as a non-native error, because the こおり spelling for 氷 is fixed and well-known.
It’s worth noting that Japanese people can struggle with this, too. There’s a fairly well known mnemonic sentence taught to Japanese schoolchildren that helps with this. It goes 遠くの大きな氷の上を、多くの狼が十ずつ通る。(とおくの おおきな こおりの うえを おおくの おおかみ とおずつ とおる。）It contains the most common instances of kanji that use おお instead of おう. So while some people might have the reaction Belthazar mentioned, I’m guessing parents and elementary school teachers might just recognize your mistake (IME generally won’t, though.)