Will my area be getting an nbn broadband access network connection if we are already serviced by another telecommunications provider?

No, to submit a new development application with nbn, you must not be in agreement with other telecommunication providers to service your development.
This is outlined in the Federal Government's Telecommunications Infrastructure in New Developments Policy that intends to ensure that networks that are considered to meet all the necessary nbn™ standards are not overbuilt by the nbn™ access network.