Yes, You are using an offensive action (I'd also rule that it would end Sanctuary).
If a cleric casts Invisibility on his or herself, then uses their Channel Energy supernatural ability to cause damage to an undead creature, does the cleric become visible?
Yes. See the bolded bit below. While it doesn't call out channel energy, channel energy is a Supernatural ability that damages foes in an area. That makes it an attack.
For purposes of this spell, an attack includes any spell targeting a foe or whose area or effect includes a foe. Exactly who is a foe depends on the invisible character's perceptions. Actions directed at unattended objects do not break the spell. Causing harm indirectly is not an attack. Thus, an invisible being can open doors, talk, eat, climb stairs, summon monsters and have them attack, cut the ropes holding a rope bridge while enemies are on the bridge, remotely trigger traps, open a portcullis to release attack dogs, and so forth. If the subject attacks directly, however, it immediately becomes visible along with all its gear. Spells such as bless that specifically affect allies but not foes are not attacks for this purpose, even when they include foes in their area.