Unfortunately it is possible to get the credentials but you won't be able to use them to authenticate to the Sharepoint Server, at least in the online versions.
We had a similar scenario but in the end we had to use a special user to do all the work in sharepoint, we were triggering the code with a plugin and using the REST Endpoint to do the work.
You can access the the User Credentials from the localContext, but you won't be able to retrieve the password.
Is your environment onpremise or online?/