First off, I will note that if the Pluto/Charon system could retain trojan objects in its L4 or L5 points, they would not last more than a couple centuries due to the fact that those points pass close enough to Neptune to throw any trojan objects off course. But that is not what this question pertains to.
Given the large differential between the mass of Pluto/Charon and the size of its orbit, is there enough influence from Pluto/Charon to establish significant, stable heliocentric L4/L5 points? Is there a threshold value of mass-to-orbit where these points simply disappear?
And the other half of the question: what is the effect of a highly elliptical orbit on lagrange points? Are they transient, only existing for a short time when the angle of incidence matches up with the gravitational effect, and would the motion of the primary system (and hence its lagrange point) draw an object onto a stable path (assuming it was sufficiently massive)?
If Pluto/Charon is capable of lagrangian capture, and the objects it captures always eventually get perturbed by Neptune, might this act as a sort of engine for moving stuff inward in the solar system?
And do the mechanics of Pluto/Charon sort of apply in reverse to Mercury, which is small and has a very eccentric orbit?
Do you want objects orbiting around the Sun, leading and trailing the Pluto/Charon system, or do you want objects orbiting Pluto, leading and trailing Charon?
I imagine Pluto/Charon have fairly strong lagrange points WRT each other. I refer to them together because, as Ruken noted, the barycenter of Charon’s orbit is outside of Pluto. I see both of them together as comprising the primary mass that any heliocentric lagrange points would reference.
According to Wikipedia, the Pluto/Charon mass ratio is about 9, not large enough to make L4 and L5 in Charon’s orbit dynamically stable. Stability requires a mass ratio greater than about 25.
There was an old Asimov story where the bad guys tried to hide by putting themselves in a Trojan point of a binary star and turning off all ship electrical for a few days - only to discover when the turned this on that they were way out of their planned orbit, falling into one of the suns. Asimov mentioned then that Trojans were unstable if the mass ratio was too close to even.
The whole kerfluffle with stripping Pluto of it’s classification as a planet was based on the new standard of “has to clear all other objects from it’s orbit around the sun”. If Pluto/Charon isn’t massive enough to do that, I doubt it could have a heliocentric L4/L5.