Using a Kalman filter to predict samples between measurements
I'm sorry that it was not very clear to me what you were asking. But I think I have developed some sense on it as follows: 

You are physically capturing 10 noisy sensor measurements per second, which I call it as the physical measurements. But for some reasons, you want to fill in between those true-physical data samples with new synthetic data, generated mathematically at a rate of 100 samples per second (10 times more dense than available with the physical sensor measurement)

The solution to this problem has different names, based on your interpretation and which method you choose to follow, such as a sampler, a  predictor, an estimator, a curve fitting or an interpolation...

It seems, you want to use a Kalman filter (an estimator actually) to generate those new synthetic samples in between the true physical measurements. And your question is whether you should feed those synthetically generated new sampes back into the Kalman filter (for residual calculations) as if the data were generated from a true physical sensor, so that the filter can use it in residual calculations to get rid of the noise present in it and refine the state estimates?

That's what I understand from your question set up and my answer to it is no you cannot. Those new data cannot replace true phsyical measurements. They do not involve new information that's called as the innovations process of a random process (that you're trying to estimate), hence they cannot be used to make refined computations or decisions alone.

In fact, the Kalman filter will only propagate the current state $X(t)$ into the next phsyical measurement point $X(t+T_s)$ by using the system dynamic matrix alone. (i.e., it will solve the differential equation numerically based on the initial condition provided from the previous state estimate, and sample this solution at the requested high data rate)