You will be able to use your old phone service up till the day the line is connected (Amnet will advise you of the ETA during the provisioning process).
Unlike some other providers, if you have an existing ADSL service you will be moved to a transitional ADSL 1 service before being moved onto ADSL 2+. As a result you will experience no more than a few hours downtime (once again Amnet will advise you on which day this will occur).