Nope. And here's why:
A transformer supplying a three-wire distribution system has a single- phase input (primary) winding. The output (secondary) winding is center-tapped and the center tap connected to a grounded neutral. As shown in Fig. 1. either end to center has half the voltage of end-to- end. Fig. 2 illustrates the phasor diagram of the output voltages for a split-phase transformer. Since the two phasors do not define a unique direction of rotation for a revolving magnetic field, a split single- phase is not a two-phase system.
You have two by splitting the single phase of 240 via one hot and one neutral, but you do NOT have two phases. No revolving magnetic field. No phase A, Phase B. Single phase is all you have.