If you want to get pedantic, yes. However, the intent of what you are doing is, in my mind, much different. Logging into a system expresses the intent to run

If you want to get pedantic, yes. However, the intent of what you are doing is, in my mind, much different. Logging into a system expresses the intent to run something there - you want to perform some actions as a result of authenticating - it's an active process. Signing a document is about authenticating the document - it's something passive.