Can SEO redirects be imported via the Shopware API?

Yes, SEO redirects can be imported via the following Sync API call: 

POST https://www.my-shop.com/api/_action/sync
[
 {
 "action": "upsert",
 "entity": "acris_seo_redirect",
 "priority": 1,
 "payload": [
 {
 "id": "1901dc5e888f4b1ea4168c2c5f005540",
 "active": true,
 "oldUrl": "/old-url",
 "newUrl": "/new-url", "
 " "searchUrlBy": "old_url"
 }
        ]
    }
]