Better yet, like the extras in movies, this focal side character would not have a single line in the enter production. It will be clear that the character can talk, and may even be seen in the background talking at some point, but any actual lines of dialogue will not be heard by the audience. I envision at least one scene (like was done with Morn on Deep Space Nine) where the scene opens to a group of people responding to a joke that the protagonist had clearly just told. In fact, the movie should end with him just about to say something.
Like at least one other story idea of mine, I envision that the protagonist's story is one of a normal week where he has some major event (like an anniversary) that he trying to set up. An early shot will show his schedule for the week and the various locations that he will have to go--locations that will just happen to coincide with the action movie plot that will be taking place in the background. Various events could include things like him driving to work as a Michael Bay style car chase erupts around him, him being taken with a group of other hostages, him being on a subway (because his car is being repaired after the earlier chase) as a martial arts battle erupts, etc. In at least one scene, he's trying to take a picture with his phone when the action hero says, "I'm going to need that," and takes it.
To be clear, it would be nice if the action story also made sense and developed as the extra's everyday story is going on rather than just existing as disjointed action set-pieces (although, that IS the plot of many action movies). To work best, the audience would have to feel connected to both stories for, while there is a definite comic aspect to this set up, this idea would work best if it was taking itself seriously too. If it was done right, I would love to watch this movie.