I want to use a trigger or automation to respond to customers in order to to avoid a breach of our SLA targets such as the first reply time. Can an email from a business rule satisfy SLA targets for wait time?
No. An email notification from triggers or automations does not count as a public response. First reply time and Next reply time target ends when a public response from an agent is recorded. Consider Answer Bot for your automated email response instead.
For more information about SLA targets, see the article: Defining and using SLA policies (Professional and Enterprise).