No. Spells Known is a part of the Spellcasting or Pact Magic features. Any spells granted from other features do not count against this limit, unless explicitly stated.

The premium Player's Handbook stealth erratas divine power

The 4th-level Clr spell divine power [evoc] (Player's Handbook (2003) 224) has as its description the following:

Calling upon the divine power of your patron, you imbue yourself with strength and skill in combat. Your base attack bonus becomes equal to your character level (which may give you additional attacks), you gain a +6 enhancement bonus to Strength, and you gain 1 temporary hit point per caster level.

(This is also how the System Reference Document presents the divine power spell.) The premium edition Player's Handbook (2012) has a nearly nearly identical description of the spell except that its description addresses exactly the question's point:

Calling upon the divine power of your patron, you imbue yourself with strength and skill in combat. Your base attack bonus becomes equal to your character level (max. +20; which may give you additional attacks), you gain a +6 enhancement bonus to Strength, and you gain 1 temporary hit point per caster level. (224 and emphasis mine)

(This bibliophile finds the abbreviation amusing: Had the word maximum been spelled out rather than abbreviated the page layout would've been utterly fouled and someone would've had to've gone in and touched up the layout on, I imagine, the remainder of the Spells chapter, likely requiring more money than Wizards apparently wanted to spend on what is largely a reprint.) A similar stealth errata was inserted by the premium edition Player's Handbook into the 6th-level Sor/Wiz spell Tenser's transformation [trans] (PH 294), around which similar controversy swirls. (To be clear, though, the transformation spell says, instead of max. +20, max +20 (n.b. no period—gasp!). I'm certain that right now a lawyer's arguing in his brief for gamer court that the max +20 phrase is meaningless because the word max when not an abbreviation isn't a game term. Good luck and godspeed on that, Matlock.)

If the campaign does not follow the rules for primary sources or no one has access to the premium edition Player's Handbook, I agree with this answer: the divine power spell works like it says it works, setting the creature's base attack bonus to its character level even if that base attack bonus would exceed +20 but even a seemingly too high base attack bonus not allowing more than 4 base-attack-bonus-derived attacks during, for example, a full attack. However, the spell granting a seemingly too high base attack bonus is no longer an issue with the premium edition Player's Handbook available.