Is Henry's Law sufficient for calculating CO2 solubility?
There are multiple forms of Henry's law (see this Wikipedia entry). The net or effective Henry's Law takes into account the other pH-dependent equilibria of $\ce{CO2}$ and carbonate species in water (chemical reactions with water in your question).  

In the case of blood, as you said the picture is even more complex. You would have to be careful using, for example, published values of the effective Henry's Law solubility of $\ce{CO2}$ in that case.