Yes, only Jira sites that have the Synchronize Attachments toggle enabled on the Connections page will have the attachment synced from the associated issues and Salesforce objects.
If there are two sites connected in the Salesforce environment, Jira Site A has turned on the Synchronize Attachments and Jira Site B turned it off, then Salesforce will only push/pull attachments from Jira Site A and not Jira Site B.
For more information on how to configure the attachment syncs, read Working with attachments in Salesforce.
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