Warlocks can take quicken spell-like ability: eldritch blast (MM p.304) at 10th level (really 12th level due to feats from level progression). And from everything I've read, modifiers on eldritch blasts do not change the fact that it is an eldritch blast so you don't have to take the ability for different combinations of eldritch invocations applied to that eldritch blast.
However, there is a potential issue when reading the description for Quicken Spell-Like Ability in the monster manual:
The creature can only select a spell-like ability duplicating a spell with a level less than or equal to half its caster level (round down) –4.
The issue is this: When selecting blast shape and essence invocations, they affect the level of the spell-like ability. So while you can learn quicken spell-like ability for eldritch essence (because it is level 1), casting an Utterdark Blast is a level 8 spell-like ability. It is unclear if a creature is allowed to actually quicken that application of the eldritch blast, or if they can only quicken applications of eldritch blast that still conform to limitations set by the caster level chart on page 304.