Can Substances on Titan be Reacted at a Thermodynamic Gain?
The thermodynamic problem is not so much with the hydrocarbons reacting with O2 as it is with forming O2 from water.  That reaction is energetically uphill.  A big hill.  In fact water is a waste product of your second reaction.  The reason the second reaction is energetically favorable is due to the high stability of CO2 and water relative to the reactants, methane and oxygen.

Would it make sense that you should be able to then convert the water from your second reaction into O2 and H2 in a way that would consume less energy than it took to make the water in the first place?  That is almost equivalent to what you are proposing by starting out with the water already present on Titan.  

The prohibitive energetics of your reactions apply on Earth as well as Titan.  You need a process to split the water to burn with hydrocarbons that will consume less energy than the energy you will get back from burning the hydrocarbons.  You could conceive of using solar power as the energy source for converting water into O2 and H2.  Or other energy sources.  But that wasn't your question, and you definitely won't get the energy back that you would require via your second reaction.  And good luck with my solar energy idea on Titan ;)