Microsoft Exchange Online uses the Tenant External Recipient Rate Limit (TERRL) to limit the number of external recipients a tenant can send emails to within a 24-hour sliding window. The limit is based on the number of Exchange Online or Exchange Online Protection licences assigned to the tenant.
Are emails processed by Crossware counted twice?
No.
According to Microsoft, emails that are sent to an external recipient and routed through a signature service or an on-premises mail system before returning to Exchange Online for delivery are counted only once towards the Tenant External Recipient Rate Limit.
Microsoft notes that these messages were previously counted more than once in some scenarios, but this behaviour has been corrected.
If I send a message to an external recipient but it routes out to a signature service or on-premises for processing, then comes back into Exchange Online to be sent out to the external recipient, will that get counted twice?
We were counting these messages more than once earlier. But now we fixed this issue and email is counted only once.