Pragmatically speaking, you need two things to fly GPS approaches to LPV minimums... GPS (obviously) and the ability to detect if that signal is degraded or inaccurate.
That's where RAIM comes in. It doesn't make the approach any more accurate, but it does allow you to check the validity of your calculated position.
You can calculate a good fix from six or nine SVs, but you need 24(23?) for RAIM to work. You can calculate in advance whether you'll have that many, which is why you have a note to that effect.
Honeywell FMS on the Airbus can do the calculation for you. I've never seen it come up with a negative answer, but you'd expect good coverage at middle latitudes in the northern hemisphere.