Yes—based on the community answer, Picasa lets you download individual images or entire albums back to your computer if you have the Picasa software installed.

To do it, open an online album and use the Download button above the images. One option is Download to Picasa, which downloads the album into the Picasa application on your computer.

What’s supported from the provided answer:

• download single photos or whole albums
• download them to a local computer via Picasa software

What’s not confirmed by the answer:

• whether all tags/metadata are preserved
• whether online album structure is perfectly recreated locally
• whether original or resized files are always downloaded

So, the reliable takeaway is that you can download albums or images back to your computer through Picasa, but you should verify metadata and file-size details after downloading.