Does sulfuric acid formed in a previous step dehydrate a secondary alcohol?
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.