To prove Turing-completeness, is it enough to prove capability of producing arbitrary output?
Turing-completeness means that the machine model in question can compute everything that is computable. That means that for every computable function $f$, there is a corresponding program for your model which behaves "like" $f$, where I put the quotes since the input and output may look differently.

Showing that the machine can generate arbitrary output is hardly enough - consider the machine model which executes only one program, copying its input to its output.