The topic of my study is Emotional communication. Categorical measures of emotional somatic and facial expression will be assessed with the STAI serving as the outcome variable in the AVONA.
I would say no. They should not be summed. STAI Trait measures approximate to measures of neuroticism, whereas state scale measures current level of anxiety. They are measuring different things and so shouldn't be summed as their product is not a "longer" scale with greater range. To mean the result is fairly meaningless because you don't know what you are measuring precisely. In fact we should be moving towards greater precision in psychological measurement rather than less. Most of our questionnaire measures are already way too imprecise.
@ Richard: Another reason I wanted to sum the State and Trait components of the STAI, is due to Izard's theory that both past and current events influence emotional processes. For example, one's emotional reaction to a dog, depends greatly on past confrontations with dogs. By the same means one's emotional reaction to a stimuli should be associated with both State and Trait Anxiety.
I also would say it is problematic to combine state and trait scores from a theoretical point of view. And while your reasoning that also past behavior influences current behavior makes sense, this could be mediated by the current state.
Why you want to create a "larger range" anyway?
Just a side note: If you are mainly interested in anxiety, then the STAI is not the best measure (since it has bad discriminant validity regarding depression and anxiety).