Young's modulus of steel is liable to change depending on its carbon content as it is the case for any other solute. How it will change though, is not really straightforward as it will depend on how you heat treat the metal and the phases you form.
Now, you mention strength in your question. While alloying is clearly a very effective and potent strengthening method, it has only a limited impact on Young's modulus. For steel, the modulus is about 200 GPa +/- 10%, even when heavily alloyed (stainless).
Modulus of elasticity changes slightly with the variation of Carbon. But the magnitude of all steel is about 200GPa. It can vary from 190GPa to 210 GPa in all possible variation..