Surely for the player. . . perhaps perception of the audience would further inform the affect on sound of increased or decreased pressure on the instrument by the player. It would seem interesting, at some point in such a study, to include perceptions of an audience and compare the data.
Both player and audience would be interesting to look at. So you'd be trying to determine a relationship between the actual grip strength (which could probably be measured in force) and the perceived loudness of the instrument? It would also be cool to measure the actual loudness as well, perhaps.
Loudness, yes...but expression as well...if the player applies more force, does that translate as 'forte' to the listener...or expressivo...or conversely less force, piano, cantabile etc. Does more force indicate more intensity? The audio wave could be analyzed with software and force plates could be attached to a fingerboard to measure applied force. The question is, what is the perceived affect of greater or lesser force applied to the instrument for the player and for the listener?
It would be reasonable to assume some relationship between force and expression, I think. The intriguing part would be the nature of that relationship and perhaps also how it varies over different genres. So the big question: if we determine the relationship what problems does it solve? There are surely applications in performance, training of musicians, for example?
From my point of view as a performer/pedagogue, the ramifications could inform both teaching and performance practice. Since there is strong evidence that the physical nature of playing music poses dangers to the body (and, sometimes, the mind), there is always a quest to perform most efficiently with the least physical and mental exertion. However, the affective nature of live performance might be informed as well. If we discover that increased force has an effect on how an audience perceives a performance then intentional changes in applied force might be developed, in a manner that does no harm to the player or the music as well, so as to add to the performance experience for the player and the audience.