No, we do not currently have any official integrations with Translate & Adapt, and our Shopify plugin does not support any third-party apps.
For supporting multilingual search using our Shopify plugin, we recommend exploring our Shopify Markets Indexing feature.
If you are not using Shopify Markets, you can use metafields or named tags to add translated data for the product. This allows you to display the translated product information on your frontend using the specified attribute.