Yes, what you are seeking to do is possible, and the Flow would look something like this: 
In the Recurrence you could set it to run weekly. In the Get items you call the SharePoint List, and the Create table points to an existing Excel file. You'd then use the Send an email (V2) to send the email with the spreadsheet attached.
If you'd like the Excel file to be empty, you can add a Get tables step, and a Delete tables step, to first clear the spreadsheet before adding the new table.
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