No, you won't.
If you have a dual-trace scope, connect the common lead to L1, connect probe 1 to the center tap and probe 2 to L2.?? You'll see both traces are in-phase with each other. What you find is that you have a single phase that's been split down the middle. NOT two seperate phases. Credit to rob for the simple way in which to verify this. Phases are offset from one another. A split single phase setup is NOT offset. You incorrectly assume that because you have two
120volt wires feeding that outlet that you have two phases from a single phase pole transformer, but, you do not. OTH, If you have a hot coming from one transformer and another hot coming from yet another transformer, then, yes, you have phase A and phase B. They will be offset and you can confirm this with a dual trace scope.