No. The field coil makes an electro-magnetic field in the alternator, without which, the alternator will make no output. The white wire powers the field coil. Some regulators are designed for bikes that have permanent magnets in the alternator and therefore supply no power for it.
I'd guess your donor bike (whatever that is) used a permanent magnet in the alternator and it's regulator won't function as you hoped in an SOHC4.
Cheers,