I don't have experience with applying to either institution via this test, but I do have experience with the test itself.

Based on what I can see on the respective websites, it seems to me that the WIAT-4 would be relevant to the Davidson Academy only if you wait until at least third grade to test, since the scores must be no more than three years old, and the school starts at sixth grade. Plus, the performance level needs to be at a late middle school level, so you may or may not want to test him that early for that purpose.

For CTY, you can have him take the SCAT as early as grade two for their programs, which might be useful for your homeschooling efforts.

But if what you want to know is where he is at that point, rather than obtaining qualifying scores for a program, then you could certainly have him take the WIAT in two or three years as a kind of benchmark for homeschooling purposes. It may be helpful to understand that the test is designed to place a student ordinally in the population of their age-peers, rather than to identify their age- or grade-equivalence (notwithstanding the presence of scores with those labels). That is, the percentile/standard score numbers are the highest-quality measures. Related to that, it's best not to readminister it too frequently (best practice is no more than every six months, and typically, quite a bit less frequently than that). So if you think you will need a good administration of it at some specific point in time (say, the summer entering grade five, preparatory to a DA application for grade six), then it might be advisable to plan the previous administration for at least a year or two prior, for maximum utility and minimum retest effects.
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...pronounced like the long vowel and first letter of the alphabet...