Probably not in any practical, complete way. Picasa's picasa.ini format and edit pipeline are proprietary, and there is no public specification or compatible API that lets other Linux editors reproduce Picasa's non-destructive adjustments accurately.

Even if parts of the INI file can be decoded, translating those edits into another editor's instructions is unreliable because each program uses different image-processing algorithms and parameters. So tools like Darktable or Shotwell generally cannot import Picasa edits and render the same result.

What may be transferable are library metadata items such as keywords, captions, stars, albums, and folder structure, but not the actual visual edits in a faithful way.

The practical workaround is to export your edited images from Picasa as high-quality JPEGs, or TIFFs if you want maximum quality and have the storage space, while keeping the original RAWs or source files as your archive.