Does destroying additional demon altars generate more cobalt / mythril / adamantite?

Yes, this is indeed the case. The more Altars you smash, the more hardmode ore your world will have. Note that every ore cycle yields less and less ore — fewer veins are generated each time, plus they have a chance to generate inside already-existing deposits.

Smashing a Demon Altar actually does 3 different things, provided you've unlocked hardmode:

1. Adds a bit of the ore named in the broadcast message to your world.
2. Summons a few Wraiths to your location.
3. Has a chance to either corrupt or hallow a random part of your world by planting a single block of Pearlstone or Ebonstone/Crimstone.

From the Terraria Wiki [http://terraria.gamepedia.com/Altar]:

Hardcore Altar smashing ore spawning/progression:

1. Smashing 1st altar: Cobalt or Palladium Ore, chosen randomly.

2. Smashing 2nd altar: 1/2 the ore spawned from 1st altar; randomly either Mythril or Orichalcum Ore.

3. Smashing 3rd altar: 1/3 the ore spawned from 1st altar; randomly either Adamantite or Titanium Ore.

4. Smashing 4th altar: 1/4 the ore spawned from 1st altar; Cobalt or Palladium (same as 1st altar).

5. Smashing 5th altar: 1/5 the ore spawned from 1st altar; Mythril or Orichalcum (same as 2nd altar).

6. Smashing 6th altar: 1/6 the ore spawned from 1st altar; Adamantite or Titanium (same as 3rd altar).

7. Smashing 7th altar: 1/7 the ore spawned from 1st altar; Cobalt or Palladium (same as 1st altar).

...and so on; 1/8 then 1/9, etc., rotating between ore types in the same progression as above.

These hardmode ore spawns will never overwrite existing Minerals or placed Wood block squares; they only transmute biome blocks (Dirt, Mud, Stone, etc).

The answer from 'a cat' includes some of the effects from smashing altars other than this "ore transformation" effect (such as the spawning of Ebonstone, crimstone or pearlstone from rock tiles and the cration of their related biomes), but not mentioned by him are the start of random mechanical boss spawns and the trigger of possible Pirate Invasions.