Yes! Search for your data on https://almascience.org/aq, select the data you are interested in, click on 'Explore and download' and then use the small triangles in front of the '*auxiliary.tar' and/or '*001_of_001.tar' files to get access to the individual files. These can be either selected for download via the checkbox or you can use the browser's right-click and 'Save as ...' to download the file through the browser.
For Cycle 0, in order to easily find which tar files contain the actual images, this page has been created. Also, the externally developed package astroquery can be used to download Cycle 0 tar files and extract the FITS files.
Archive data products are described in How are ALMA data products packaged?.