This is a very interesting question. There are certain "classes" of words where I don't think native speakers would have this problem at all. I doubt anyone would read 父 as just 「と」, or 大 as just 「お」, unless it was being used cleverly in a number.
However, I think when using okurigana for verbs one is more likely to be confused/unsure. Sometimes it is more of a stylistic choice than confusion. For example, take the word 「うけつけ」. When written with kanji, it has four "acceptable" forms:
Depending on the context where it appears, one may be preferred over the others. I'd be willing to bet that in pure verb-usage, the "correct" form would use both けs. But even I'm not positive on that.
But then there are times that can cause genuine confusion. For example, take the verbs 「[逃]{に}がす」 and 「[逃]{のが}す」. Though they have very similar meanings, there are also nuances of each. But since they both end in 「がす」, you'd better believe that even native speakers will occasionally mix up their readings.
(Protip: The にs — [逃]{に}げる and [逃]{に}がす — both have two-kana okurigana; the のs — [逃]{のが}れる and [逃]{のが}す — have the が as part of the kanji.)