No. Shuttle stores each Etsy review only once. If you store reviews again, Shuttle updates the reviews it already has. It does not add copies.
Shuttle also keeps track of which reviews you have already exported. What ends up in your export file depends on the option you choose.
Choosing which reviews to export
When you click Export reviews on the Reviews page, Shuttle asks Which reviews?:
All reviews: every stored review, including reviews you exported before.
Only non-exported reviews: only reviews that have not been exported yet.
By a date range: every review between the dates you pick, including reviews you exported before.
If you have already imported earlier reviews into your reviews app, choose Only non-exported reviews. Then the new file holds only reviews your reviews app has not received yet.
If you want a full copy of everything, choose All reviews or By a date range. Previously exported reviews will be in that file again.
Automatic exports
Automatic exports only include new reviews that have not been sent before. Reviews sent in an automatic export email still show as not exported, though. So a later manual export with Only non-exported reviews will include them again. If you already imported the automatic export file, take those reviews out of the manual file before you import it.
For more on exporting, see Exporting Etsy Reviews to Shopify and Automatic Etsy Review Export & Management.