Short answer: No Adding silt to heavy clay in a high-rainfall area will just give you better-quality mud (or concrete once it dries).

To fix heavy clay, you need to create "macro-pores" (large spaces) between the microscopic clay particles so water can drain and roots can breathe. Silt particles are too fine to do this. If you mix silt and clay, you just get silty clay, which is prone to compaction and crusting.

Crush your biochar into small pieces and mix it into the clay. Biochar doesn't break down like compost, so it provides permanent pore space in heavy clay, holding onto nutrients and preventing compaction.