Civilization – If you destroy a civ, do you still get the “You declared war on our friend!” penalty

I have seen a devastating rush by the Mongolians under Kublai Khan:

• Keshiks are fast. You can not understand what "ignores terrain movement costs" really means until you have played with them.
• Aggressive helps with faster Barracks
• Creative helps get horses sooner, if they're close.
• Creative helps solidify your newly conquered territory surprisingly fast, with working the best squares, providing city defense, and keeping your troop supply costs down.

You should also look at anyone else with a fast ancient era unit:

• Persian Immortals
• Aztec Jaguars
• Egyptian War Chariots

Although winning in the first attack is ideal, fast units provide the option to setup a later win. Take workers, pillage improvements, hit the weaker cities behind the lines. In the ancient era Civs don't have the numbers of units to deal with harassing enemies, and small injuries like a lost worker affect the whole game.

Note: My info about specific civs is based on BtS. I can't recall anything being different in Warlords or vanilla, but I have not checked.

As far as I know, there isn't. You should just learn to ignore it completely, no other way apart from moding.