Azure Functions - using appsettings.json
For your needs the answer is YES! Azure Functions can use appsettings.json for your configurations. But there are some ordering sequence that Azure will do when a Function is requested.
1º) Azure will look for that KEYS that you used on .GetEnvironmentVariables("[KEY]") method, through Keys that were configured on Application Settings blade in Azure Functions settings
2º) If Azure wasn't able to find out that configurations through Application Settings keys, then Azure will try looking for after appsettings.json file into your root folder of the Function that you working on.
3º) Finally, if Azure wasn't able to find out this keys either on Application Settings neither on appsettings.json file, then Azure will do the last attempt to find out web.config for looking for into this file appsettings section keys.
For your appreciation, you'll able to find out these configurations by the sample on my github repo: here and here
I hope that these information help you.
According to the changes made to the configuration files, you should only use local.settings.json since the appsettings.json was renamed to local.settings.json
Reference to the change: azure-functions-cli