What would happen if equal to Charon's mass was added to the dwarf planet Pluto?

Your question is confusing. Add the mass? The system already has a combined mass. And if you’re asking about a body of the mass of Charon and Pluto combined, the center of mass is should be rather easy to predict. Or are you asking about combining a body of Charon’s mass with Pluto while Charon remains in orbit?

Combining a body of Charon’s mass with Pluto while Charon remains in orbit…

I am guessing that Charon’s orbit would start to decay, and it eventually would crash into pluto.

I don’t understand your question but I can answer #3 (yes), and #4 (no)

Do we wave a wand, and the mass appears? The center of mass, of course, moves in toward Pluto. I don’t know the mechanics, but like Loli My guess is the moon will spiral inward. Does any one know if the extra mass might accelerate the moon in its orbit, with a shot at achieving a stable orbit?

1. Where would the center of mass be of the Pluto-Charon system?
The exact answer depends on where you add the mass. It would be at the proportional average of the distribution of the mass, as will all other connected bodies. But the change would be very small.

The mass of Charon is 6.5 orders of magnitude smaller than Pluto , so it’s less than one millionth the mass of Pluto. If you add a new Charon’s mass to Pluto, you change things by less than one one-millionth. If you just move Charon to Pluto, that’s not changing the mass of the system – just moving its center slightly.

2. What would happen to the moons?
Almost nothing.

The moons of Pluto would have their orbits altered very very slightly.

If you’re just moving Chaon onto Pluto, Charon was already inside the orbits of the other moons , so you’re only very slightly changing where the center of mass is.

If you magically added mass to Pluto without removing Charon, the effect would be to slightly increase the gravitation but only extremely slightly, so the relative orbits would stay roughly the same but a tiny bit faster and closer.

3. Would Pluto remain a dwarf planet?
Up to whoever invents the categories and their definitions, but yes.

4. Would any other orbits be affected?
Not materially.

If you want to see for yourself, you could try Universe Sandbox

Wow, at least you understood the question… :D Thanks!