Are the CTs being used for metering or protection.
CTs have a rating called "rating factor"...official name continuous thermal rating factor. This is how many times the rated primary current that the CT can operate at continuously without thermal damage.
For metering CT, it also defines the top limit of the accuracy class.
For instance, a 600:5A CT rated RF=2.0 and accuracy of 0.3B0.5 (IEEE rating) is guaranteed to maintain a 0.3% accuracy performance from 600A to 1200A (rated current up to rating factor) and 0.6% accuracy performance from 60A to 600A (10%rated to rated current). For metering applications, it's a common mistake to use to high of a ratio. 600V CTs for metering normally come with rating factors of 3.0 or 4.0. If the max current is 600A, the best way to meter is with a 200:5A CT with a rating factor or 3.0.
If the CTs are for protection, then you need to educate yourself on the protection ratings of whatever standard region you're in. But in short, no a protection-rated CT won't saturate at or near rated voltage, assuming the rated burden is not exceeded.