Operators do not 'roam' (generally) on other operators within their home country. So, yes, if you buy a SIM from either Vodafone or Telstra you will have a connection.
In our case: We have actually very bad connectivity in NL due to no signal from KPN, but plenty from T-mobile and Vodafone, but as soon as we leave the country, for example Germany we can use any operator that is available basically.