I would say yes, because I don't think that a standard action requires all that much patience, and a supernatural ability doesn't require concentration (CRB p. 186, Use Special Ability).
Can a cleric use channel energy when is in rage?
It's not explicitly called out but it appears barbarians a} can use supernatural abilities and b} can do some things that are offensive in nature. I would say yes, because of the following example which is not terribly dissimilar from channeling energy.
From the APG,
Energy Eruption (Su) While raging, the barbarian can
absorb energy from a single attack and unleash it upon her enemies once per rage. She does not make a saving throw against the effect but takes no damage from it. At any point during the remainder of her rage she can unleash the stored energy as a breath weapon in either a 60-foot line or 30-foot cone. The breath weapon inf licts damage equal to the damage from the attack absorbed by the barbarian, but creatures within the area may make a Ref lex save (DC 10 + 1/2 the barbarian’s level + the barbarian’s Constitution modifier) for half damage even if the original effect did not
allow a save. A barbarian must have the energy absorption rage power to select this rage power. A barbarian must be at least 16th level to select this rage power.