Oh good Kriston, something I can help *you* on!
First of all, eye docs (all kinds) can test kids that can't even respond. They can test 6 month olds, which is what the optometry association recommends for first vision check. My daughter has seen an ophthalmologist for vision related issues since she was three months old. She's just turned 4 years this month. The doc uses pictures instead of letters and numbers.
2nd, most eye docs don't worry about vision issues related to near vision and reading before the age of 5 because that's when most kids start to read and do more near work. But a GT kid may in fact be held back by the vision issues if not diagnosed. Also, most kids stay slightly far sighted until pre-school age or later, so they often aren't concerned. But, a GT kid who might otherwise be reading or doing near work can't if they are far sighted too badly.
3rd, some visual efficiency skills don't develop until the age of 7 or 8. Efficient visual saccades for example, rapid fixation between targets, is slower to develop than visual tracking. Saccadic movement is what we use to read. Likewise, some perceptual skills develop slower than others. So, yes, there might be some areas that are not developed to allow for reading or efficient visual processing or perceptual skills and they might just need more time.
I would suggest that you locate a couple of developmental optometrists and just call them to see if they would do an exam on a 4 year old. I can't imagine why they wouldn't. If you have coverage, you should just go. You'd only need a referral if your insurance required it. Otherwise, it's no different than finding an eye doc for yourself. I say go for the exam and rule out any problems. Ruling out is always a good thing!
