I had my rear brake suddenly drag last fall requiring me to ride home 2-up and return with my trailer to fetch the X. By the time I returned the brake was free, but damage done, the rotor was showing bluish discoloration from overheating and it obviously could not be ridden till it was fixed. I parked the bike for the winter and just got around to tearing into it today.
Dave McMunn had previously swapped me a complete newly rebuilt 2-pot rear caliper and a like-new Prolink rotor in exchange for some H2 parts a while back and I had a new brake line on hand too. My buddy Joe and I made pretty quick work of the swap, installing the new rotor and caliper, and then the new brake line. When we had it back together it was unusually slow to bleed and pump up, which in hindsight should have been a dead givaway that the problem was indeed in the master cylinder, but we forged ahead anyway. Once we had the air out I went for a short ride down the cul de sac and then out onto the road. By the time I returned from a 2-mile roundtrip it was dragging again, but thankfully I did not appear to have overheated the rotor this time, although it was good and hot. And so the bike went back onto the lift and we pulled the master cylinder as we should have from the start.
There was the usual amount of cruft and goo under the boot at the bottom, and the little reservoir in the master cylinder had crystalized brake fluid from where it was weeping past the sealing o-ring:

See the smaller of the two orifices in this pic (upper)? That's the (tiny) return circuit orifice that allows brake fluid to come back from the 'pump' part of the master cylinder, allowing the pistons to retract after the brakes are applied. If it's clogged then the fluid is slow at best to return and brake fluid can be forced past the other seals in the MC while it's under pressure and getting heated up, causing your brakes to grab and drag, and overheating your rotor, pads, caliper and the fluid. Not good.
In a pinch one could simply remove the plastic fitting that sits over this reservoir on the MC, clear the clogged orifice, and put it back on, but that's likely make a mess and the crystallized crap that caused it to clog would still be floating around in the system. Here's what that looked like on mine (note the dark flecks of crap).

So we opted to disassemble it all, clean it all out and rebuild it. But first, we had to clear out that return orifice, because it was indeed well and truly clogged. That hole should pass straight through to the bore of the cylinder: mine was so clogged I called Dave and Phil to ask if it took a 90-degree turn or something. I plucked a wire from my wire brush, clamped it into a teeny set of vice grips and twisted it like a drill. I could not simply poke it through, it was too solidly blocked. Twisting it was Dave's suggestion when I called him, and that did do the trick.

Then we honed the bore with a rotary brush in a drill, cleaned it all and washed it all with soapy water, and then dried it and set it in the sun for a few minutes to blast off any remaining moisture.

Then it was a simple job to rebuild it, install it, refill the system with fresh fluid, and this time it pumped up good and hard in a matter of 5 minutes with no weirdness.
SO...
Based on my extensive experience of this happening once, if you're dealing with brake drag, I'd do this first, give your brake system a good flush, and see if that does it before you go tearing into your calipers. I had the new parts to install anyway, so I didn't really lose much time for my efforts, but it would have worked a bit better to do it in the reverse order in my case, eg, do the master cylinder first, then go down stream.
N.