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The hardening of carbon steel highly depends on the temperature at which the metal is heated and at what rate the metal is cooled. If you do what you say you wouldn't really be increasing the carbon content of the "whole" piece, but rather just the exterior surface. It would have a sort of "carbon" case which is only good for the sharp part of the chisel. Depending on the carbon content present before quenching, the chisel will remain in different phases. The phase you are talking about, when you quench it in a relatively cold fluid (I wouldn't advice motor oil because it gives off fumes and smoke that are bad for you) to room temperature it's called Martensite, a non-equilibrium single phase structure that results from a diffusionless athermal transformation of Austenite.