SOR is only a concept that says that we have to look inside of a person to understand her. The O justifies actually the whole area of e.g. consumer behavior research. Consequently, what exactly you use to study this O depends on your research question and your hypotheses. If you study satisfaction - then measure satisfaction. If you study why people respond to facebook postings then satisfaction may not be your primary interest. In this case you would likely to look to another concepts such as emotions, intentions, pursuit of popularity etc.

So, the short answer to your question:

The choice of a construct to measure depends on your research proposal. 

Satisfaction may be added depending the variables you have selected for your model

I agree - satisfaction can be an internal reaction similar to other internal reactions e,g, emotions such as happiness or contentment. The questions is whether your research question and model sees satisfaction is a response in itself . If you treat it as the organism then it acts as a mediating variable between something that occurs in the environment and an outcome such as whether one would want to stay, leave or even come back. If you treat it as a response it becomes a reaction to the organism (experiencing positive emotions) e.g. I go to a nice restaurant - it makes me feel good - which in turn increased my level of satisfaction with the restaurant. In the latter case satisfaction would be acting as the response. You need to be clear what your final outcome is (i.e. your DV) before you can decide whether to treat it as the organism component of the SOR model.

In that case then yes satisfaction could be the organism response in the SOR model.