Starting with the required DLSR settings to take an aurora photo and working back, we can see what would be needed for a compact camera to capture such a picture.
A clear aurora photo would use an exposure of around 5-10s at f/4 with ISO 1600 - this is obviously dependent on the intensity of the aurora, so is only a guide.
If you apply the limits found on most compacts, you can manipulate the figures to see what would be required. So, if the highest feasible ISO value is 800 (without excessive noise), you would need to increase the shutter speed to between 10s and 20s to obtain the same exposure value. Equally, if the widest aperture is f/5.6, you would need to go even further to around 20s or longer. This, however, is entering into the 'too long' category, which as you rightly say would result in too much movement to get a clear picture.
So you'd need to check what your camera is capable of. Using the guideline exposure above, calculate the shutter speed needed based on the highest usable ISO and widest aperture on your camera, and decide for yourself whether it would work.