Jon,
it makes a difference, indeed.
The w/c alternator has 6 (or 5) coils in a 2phase configuration, and 3 wires color coded as I wrote before.
Different alternators were used for the N/C models. AKAIK there are at least 2 different 3wire stators, both with only 2 coils. These are arranged as 2 different power circuits. The older one was used in the 250SCR and Mk3 until a certain engine number. It has one coil for the lighting circuit, another for the ignition. Both are
AC driven, requiring a special AC ignition coil, but no battery.
The later alternator also comprises 2 coils, but for lighting and charging, respectively. The ignition is a DC type, needs the appropriate DC coil, and of course a battery.
Connecting two 6V coils in parallel to the single point in parallel may not work, especially in case of the AC ignition system, because they consume twice the power, so will overload the alternator coil and produce a weak or even no spark at all. Running them from a battery also will draw double power, but may work or not, due to the unpredictable interaction of the coil's primary windings and the single capacitor. I never made this experiment, always implemented two series connected coils, either in 3 or 6 Volt version, or a dual HT output coil.
For reference you should read through the extract from the workshop manual
http://renato2.bplaced.net/DUCATI/electrical_system-NC.pdf.
Do you remember the type of your stator (2 or 6 coils)?
Hans