Yes. The most recent releases of the Azure ImportExport tool - versions 1.5.0.300 (for blobs) and 2.2.0.300 (for files) - automatically overwrite blobs or files that already exist in your storage if an import includes a file or blob with the same name.
Earlier tool versions renamed an incoming file by default if an existing blob or file had the same name. A Disposition field in the dataset CSV file lets you specify whether to rename, not overwrite, or overwrite the destination file or blob. The Disposition field had this format: Disposition:.