In a word no.
You must use the service configuration file for such settings.
To decide on whether to place keys in the service configuration settings versus web configuration settings.
You could ask yourself the following questions:
Does this setting change with every deployment? If so then the web configuration settings is the correct place for this information.
Will this setting change after deployment? If so then the service configuration settings is the correct place for this information.
The Web.config file is part of the deployment package and so is read-only when deployed to Azure, in order to update the settings you will need to redeploy.
Whereas the service configuration file is uploaded with, but not packaged with, the deployment package, and therefore you can upload or edit the file without redeploying your service.