No.

It specifically mentions that warlock eldritch blasts and invocations are subject to arcane spell failure because unlike most spell-like abilities they have somatic and/or verbal components, albeit simple ones that can be cast while wearing light armor (or medium with Battle Caster feat).

So in that situation, no they couldn't. And since spell-like abilities are in all other circumstances non-somatic/verbal, there's no Still/Silent Spell-Like Ability feat (unlike Empower/Quicken/Maximize). So you'll never be capable of casting them in that situation.

From Complete Arcane, page 7:

All invocations, including eldritch blast, have a somatic component.

[...]

Unlike other spell-like abilities, invocations are subject to arcane spell failure chance.

The warlock's ability to regulate (to some degree) the effects of her eldritch blast (like damage) by lowering the blast's effective caster level has no impact on her ability to pick or employ metamagic-like feats related to the eldritch blast.

The eldritch blast's spell level

The warlock's effective caster level of her eldritch blast isn't the same as the eldritch blast's effective spell level. (This overuse of the word level dates to the game's inception, even inspiring a favorite Web comic strip.) The spell level of eldritch blast was changed by the Complete Arcane errata:

Page 7: Eldritch Blast

Second paragraph of the Eldritch Blast ability description: Change “An eldritch blast is the equivalent of a spell whose level is equal to one-half the warlock’s class level (round down), with a minimum spell level of 1st and a maximum of 9th when the warlock reaches 18th level or higher” to “An eldritch blast is the equivalent of a 1st-level spell. If you apply a blast shape or eldritch essence invocation to your eldritch blast (see page 130), your eldritch blast uses the level equivalent of the shape or essence.”

Any other references to eldritch blast being something other than the equivalent of a 1st-level spell should be disregarded. Any other references claiming that eldritch blast is not an invocation should be disregarded. A warlock can use eldritch blast at will. (1)

This means for most purposes except as pointed out by the errata the eldritch blast is effectively a 1st-level spell. Thus, for example, a warlock must possess at least a caster level of 6 (therefore usually being a level 6 warlock) to take the feats Empower Spell-like Ability (eldritch blast) (Monster Manual 303) and Maximize Spell-like Ability (eldritch blast) (Complete Arcane 81), and a warlock must possess at least a caster level of 10 (therefore usually being a level 10 warlock) to take the feat Quicken Spell-like Ability (eldritch blast) (Monster Manual 304).

The eldritch blast's caster level

Because, except for a few situations (like, for example, its lack of components), "a spell-like ability functions just like a spell" (PH 180), this means an eldritch blast can be employed "at a lower caster level than normal, but the caster level you choose must be high enough for you to cast the spell [i.e. employ the blast]…, and all level-dependent features must be based on the same caster level" (PH 171). Thus, a level 7 warlock could opt to employ the eldritch blast as if her effective caster level were, instead, 6, 5, 4, 3, 2, or 1.

For example, to bring this all together, if she wanted to for some reason, a level 7 warlock that possesses the feat Empower Spell-like Ability (eldritch blast) can use the feat yet employ the blast as though her effective caster level were as low as 1.