Not really. This is a plugin that stands in the middle of WooCommerce and Resurs Bank and the intentions is to only pass data from one point to another. All data and personal customer information are handled by WooCommerce and Resurs Bank explicitly.
Logged data is as of v0.0.1.2 (one of the release candidates) obfuscated, since it is not known for how long log files will be stored by merchants. Examples from the log storage (from a fixed 0.0.1.3):