Blistering Invective could be effective against Rat Swarms, but it is unlikely. Other Swarms may be immune or not, depending on their composition.
While Swarms have their own immunities:
A swarm is immune to any spell or effect that targets a specific number of creatures (including single-target spells such as disintegrate), with the exception of mind-affecting effects (charms, compulsions, morale effects, patterns, and phantasms) if the swarm has an Intelligence score and a hive mind.
You must also consider that a swarm of Rats is also an Animal creature. Luckily, being an Animal leaves them susceptible to Demoralization. However, many Swarms (including Spiders and Wasps) are composed of Vermin:
Mindless: No Intelligence score, and immunity to all mind-affecting effects (charms, compulsions, morale effects, patterns, and phantasms).
Additionally, as has elsewhere been stated, Blistering Invective is [language-dependent]
A language-dependent spell uses intelligible language as a medium for communication. If the target cannot understand or hear what the caster of a language-dependent spell says, the spell has no effect, even if the target fails its saving throw.
So an Animal Swarm could be intimidated by an area effect (but not a simple Intimidate check), but you would need to speak a language that they do (and Rats/Rat Swarms, like most animals, speak no language).