Your argument does have some merit but I prefer to believe that the GCC will ultimately be in coalition with Israel against IRAN.
They can settle their differences later after Syria and Iran are disposed.
I would suggest the buildup is to be ready for some Iranian aggressive screwup when Syria falls apart or begins to fall apart. With Syria gone, Iran is without the surrogates causing most of the problems.
Yes, I do believe you're likely right about this. Iran will not be happy about the fall Of Syria....but Syria isn't going down easily. Too many imagine this will go like Libya and a grave mistake to even think similar. It's a different beast altogether....especially with China and Russia supporting Assad.