Yes and no. The system is separate as far as fluid goes, but not heat transfer. The MC is metal, and the heat from one side will conduct over to the other side, so if it boils long enough, both sides end up boiling.
Plus, a stuck caliper sufficient to boil the brake fluid is squeezing pretty tight. You should notice at the very least a significant mpg drop, and most likely the vehicle will pull to whatever side the stuck caliper is on. (obviously, if OP has 2 stuck calipers, one on either side, then it could still be boiling fluid - but he most likely needs a new MC anyway since the seal integrity is now compromised).
On the other hand, a sinking pedal like this is a classic sign of a master cylinder who’s piston seals have either gone bad, or have gotten gunk between them and the cylinder wall and are therefore no longer creating a perfect seal.
A pretty good test for this,incidentally, is to slam on the brakes. If it’s just a bad piston seal, the brakes should stiffen up because the fluid is viscous enough that it can’t leak past the piston seal fast enough to cause a mushy pedal. If the brakes don’t stiffen up, then your fluid might be boiling (because now it’s a lot less viscous) - - of course, it no longer matters because now you’re about to hit a tree 
Long story short, I’ll keep saying what I said - OP needs a new master cylinder, and checking the rest of the braking system while it’s under the knife is a very good idea.