Yes, you can digitize well logs using Didger. You can scan the logs and digitize them onscreen, or if you have a digitizing tablet you can digitize them directly from the paper log.

We have two newsletter articles which describe digitizing well logs:

Using Didger 3 to Digitize a Paper Well Log and Export as LAS

Digitizing Logs and Exporting a Single-Line or Multi-Line LAS file Using Didger 4

The first article shows how to digitize it from a tablet and how to digitize it from a scanned image.

The second article covers digitizing a scanned image in Didger 4.

In addition to manually digitizing a log, Didger 4 also has a feature for automatically digitizing logs.  This feature is the Vectorize Image command and can be used by clicking Image | Vectorize Image.  For a better understanding of the Vectorize Image command please see this article.