We don't have any experience with the CK6414 tube, so it's impossible for us to predict its behavior in the FetValve circuit without doing a full engineering analysis. However, a quick review of the datasheet you link to suggests the CK6414 consumes appreciably higher heater current than the 12AT7. This alone makes rolling it in a circuit designed for a 12AT7 questionable at best. It also has a significantly lower maximum plate voltage than the 12AT7. Finally, it has about two-thirds the mu, and the distribution of interelectrode capacitances appears to be different. Given these, our prediction is that the CK6414 is not a good choice for replacing the 12AT7 in the FetValve circuit. We would consider any damage caused by attempting this to be outside a warranty claim.
It's also important to note that the CK6414 was designed for computer applications, not audio. This means that design and manufacturing standards that matter for audio (e.g., low microphonics) may not have been applied to the CK6414.
As Frank stated, we have been very happy with JJ 12AT7 in FetValve preamplifiers for their performance and consistency.