Yes, does work that way. It lowers your global CD on abilities with lengthly CDs since 6.0.
Haste - Wowpedia - Your wiki guide to the World of Warcraft
Starting in Mists of Pandaria, and expanding in Warlords of Draenor, many classes have received passive abilities that cause haste to also reduce the cooldown of certain abilities. [Sanctity of Battle] and Flurry are two examples of this effect.
(from wowhead cos wowpedia is wrong)
Sanctity of Battle
Requires Paladin
Requires level 58
Melee haste effects lower the cooldown and global cooldown of your
Holy
Holy Shock
Judgment, Crusader Strike,
Protection
Hammer of the Righteous, Consecration, Holy Wrath, Avenger's Shield, Shield of the Righteous
Retribution
Hammer of the Righteous, Exorcism
and Hammer of Wrath.
=> its level 58
Flurry
Requires Shaman (Enhancement)
Requires level 20
Melee haste effects lower the cooldown and global cooldown of your Stormstrike, Lava Lash, Shocks, Unleash Elements, and Fire Nova.
=> only for 1 spec of 1 class