Does the alactrity or "activation speed" stat decrease GCD in swtor?
No, the global cool down is not effected, except in the case of cast-time abilities.
Yes. As of game update 2.0 Alacrity was improved. It now affects resource regeneration and the global cooldown.
And as of game update 3.0 alacrity also affects over-time effects and everything else. A character with 10% alacrity should be 10% faster in everything.