Does sulfuric acid formed in a previous step dehydrate a secondary alcohol? In the following reaction won't the sulphuric acid dehydrate the secondary alcohol after it's formed?
It could, but the addition of water would push equilibrium toward the hydrated product, and the $\ce{H2SO4}$ would likely transfer into the water layer that you made by adding $\ce{H2O}$. 

Plus, you would only make stoichiometric sulfuric acid. Depending on the amount of water, the pH of the solution formed could be fairly neutral. Also, usually, the acid (despite being a catalyst) is used in large excess for dehydration reactions.

Therefore, it is possible (given the right conditions) but unlikely.