Welcome to TPG Community!
You have the option to keep your ADSL service with Telstra while waiting for the TPG NBN to be installed.
However, you need to clarify the cancellation process with Telstra to avoid paying for 2 services at the same time.
Yes, you may keep it first while waiting for the TPG NBN service to be installed.
Usually, the ADSL connection will be disconnected by the NBN as soon as they've started the installation.
Just don't forget to contact your current ADSL provider for further discussion about the service cancellation to avoid any issues.