I realize that ideally you would defeat an armored opponent by thrusting or half-swording into the gaps between the plates, but could blows with a sword blade also accomplish anything against mail or plate armor? Could they bruise, concuss, disorient, etc.?

Mail was susceptible to hard blows to exposed bony areas such as the skull, clavicle, knee, hip, shin, elbow, etc. Plate was pretty much invulnerable except for head blows.

I'm not an expert, but I do practice HEMA in my own amateurish way. I fought in my first tournament this spring and won 3 fights before being eliminated. Let me say this: even when being hit with a synthetic sword, you feel it. Believe me, you do feel it, especially if it's to the head. I would imagine that the blunt force trauma would be enough, depending upon where the impact took place, to disorient and confuse an opponent. One blow to the head made it ring and I needed a moment to recover. I've suffered serious bruises through modern HEMA defenses, and suffered a cracked collarbone from an oberhaw to the clavicle from a synthetic sword. I'm certain that a steel sword, "real" or feder would have done even more damage. So yes, I would imagine that the concussive effect of a sword to poorly armored or unarmored locations could seriously erode an opponent's ability to fight.

The phrase 'to give and receive blows' pops up a few times in 14th and 15th century primary sources. The same sources also mention giving blows to the head with a sword.

In the press of battle or when people raised their visor finesse may have been thrown out of the window in favor of bashing each other over the head repeatedly. You can cut someones face if he has his visor open and perhaps a number of blows could throw off helmets or cut straps and lacing holding the armor together.

Helmets of any kind -whether on a 14th century battlefield or on a 21st century hockey rink - afford poor protection against concussions. The reason being that concussions are caused not by damage to the skull, but rather by sudden acceleration of the skull relative to the brain, usually due to some kind of impact. And for those of you practising reenactment, the subtle long term effects are nasty and accumulative. Just sayin'.

Yes, a sword blade could do *something*. Plate will resist the edge of a sword effectively, but some of the concussive force is transmitted through. The armor and padding help to spread the force around quite a bit, but it isn't a force field. Think about modern Kevlar bulletproof vests. Cracked ribs and bruising are pretty common even without penetration. A cut to a breastplate may not do much, but a thrust (like with an estoc) would concentrate the force in one spot. Cuts to arms, legs, and hands could conceivably have greater effect.
(had a finger broken in sparring with blunts and armored gauntlets that way)

IIRC, there are quite a few surviving pieces of armour that show clear evidence of sword blows, and frequently they don't penetrate at all. You could extrapolate the force of said blow from the magnitude/size of the mark left.

Yes if your opponent agrees to stand still.

But I guess nobody would agree to do this on the battlefield...