Can Nintex workflow electronically sign a word document?

it depends what you are after...

if you want the who and when a document was approved, but don't care about the actual signature then yes you can do this with the update document action.  I have blogged about this here:

if you want the actual signature, more information can be found here:

http://www.nintex.com/workflow-platform/connectors/nintex-connectors