Is it possible to use warlock’s Hideous Blow in barbarian’s rage?


According to the Complete Arcane book, warlock invocations are not spells. Barbarian rage description in PHB1 says:

While raging, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except for Balance, Escape Artist, Intimidate, and Ride), the Concentration skill, or any abilities that require patience or concentration, nor can he cast spells or activate magic items that require a command word, a spell trigger (such as a wand), or spell completion (such as a scroll) to function. He can use any feat he has except Combat Expertise, item creation feats, and metamagic feats.

So, if invocations are not spells – can I use it in rage? If they are spells can I just multiclass into Rage Mage from Complete Warrior handbook? In the other words invocations are arcane spells or not?