Should I notify my business insurer even if I doubt this is covered?

Yes, and you should do this immediately regardless of how confident you feel that coverage doesn't apply, even when you genuinely expect the claim to be denied. Notifying your insurer late, even when the underlying claim ultimately wouldn't have been covered anyway, can independently void coverage that might otherwise have genuinely applied to a different aspect of the same dispute, since many policies have strict, non-negotiable notice deadlines.

The underlying coverage analysis also isn't always as obvious as it initially appears. A lawsuit framed by the plaintiff around negligent work or a negligence-adjacent theory, rather than a straightforward breach of contract, can sometimes trigger your insurer's duty to defend under a general liability policy, even in a dispute that started out looking purely contractual. Sending the complaint to your insurance broker the same day you receive it costs you nothing and preserves options you might otherwise lose through simple delay.