Aliasing is possible in any digital sampling system if it lacks an AA filter, that is well known in the signal processing field without the need to take a single shot. In the case of image sensors it will only be monochrome moire if interpolation is not needed.
I agree with Guillermo on this. In fact, discrete repetitive sampling will ALWAYS result in aliasing that is impossible to reconstruct reliably when the sampling frequency is lower than '2x the finest spatial frequency' (AKA Nyquist frequency) in the analog signal. Sometimes the aliasing will be clearly visible (as moiré or stairstepping), while at other times it will be harder to detect, e.g. amid busy other random detail. Color aliasing will usually be easier to spot than luminance alaising.
Even if the signal can just be reliably reconstructed, say with a discrete sampling frequency between 3x and 2x the finest spatial frequency in the analog signal, it may still look a bit odd. But that can be solved by upsampling.
Color Moiré is exacerbated by the different sampling frequencies and orientation between Green, and Red/Blue filtered photosites. So 4x multi exposure with full sensel shift will improve the color moiré by generating full RGB samples, but the monochrome moiré will remain if the signal is under-sampled. Adding a half sensel shift will generate a very nice roll-off towards the Nyquist frequency, which by the way is two times higher (which already reduced the aliasing risk by doubling the sampling density).
So 16x sampling is a very effective method to increase resolution,
and reduce aliasing to almost zero (especially if the sensor uses gap-less microlenses). Unfortunately multi-exposure requires impeccable technique, stationary subjects and solid camera shake reduction with constant lighting. Fewer than 16 samples per image will be somewhat less effective, but already show significant improvement with Bayer-CFA sensors.
Cheers,
Bart