Yes, you can forge it, provided your weld was good.
But, the neatest thing about the san-mai is how the two sides gradually disappear after final grinding.
So, you'll want to keep your forging to an absolute minimum, or you'll "push" the center out-of-center and then you'll have a wandering cutting edge that will be part 15N20 and part 1070 which will etch differently.
Take your time and gradually thin the blade out but do most of your final shaping by stock removal.
Try to see if you can watch the center as you go.
Most guys are using 416 stainless on the outside these days and a high carbon core like 1095. Once welded, they stick together great, but the different properties of stainless vs. simple carbon make them easy to differentiate during forging and it's easy to correct mistakes before they happen.
Your mix is going to be a little more difficult to observe.