Upsampled input to an Adaptive filter?
Prior to upsampling, you have a white signal meaning every single frequency in the Nyquist bandwidth from $-\pi$ to $\pi$ is represented. This is a requirement to obtain an impulse (because the Fourier transform of an impulse is a white spectrum). The reason that white signals are often used as inputs for purposes of system identification is that they excite all frequencies of the system. This is important when trying to determine the system's response.

After upsampling and interpolating by $N$, you obtain a sequence with a spectrum that is more or less white in the bandwidth from $-\frac{\pi}{2N}$ to $\frac{\pi}{2N}$. The rest of the band (if your interpolation filter is working correctly) will be nearly zero or null. That means that these frequencies are no longer contributing to your coefficient calculation. In turn, this means that you cannot obtain a delta function since it requires every frequency present to be represented properly. The closest approximation to a delta function that you can obtain is a sinc pulse. This is why you are observing this result.

Summary: You cannot estimate the response at frequencies that are not contained in your input signal. Your input signal and desired signal are no longer white (because they are bandlimited by the interpolation filter). Therefore, the adaptive filter does not estimate those frequencies. This leads to the sinc response you are observing which is the closest band-limited response to the true system response (a delta function).