Avoiding padding during FFT calculation
From a programming point of view I don't see any possibility of avoiding the copy operation for 1024 values because the CUFFT library expects a pointer to an array containing NX (FFT size) values. If you don't initialize all of them, the result of the FFT operation will be random.

From a DSP point of view you could easily use a 32- or even 24-FFT without loosing information. Zeropadding in time domain corresponds to an interpolation in frequency domain, where the interpolated frequency bins can be different from the actual spectrum. You should check if you really need the frequency resolution of a 1024-FFT.