As I understand it you are essentially correct in how Apple/Google intend the system to be used, but the UK for example doesn't have the same privacy protections we enjoy in the U.S. so the implementation and what transpires when someone tests positive may be significantly different depending on the national ethos.
My assumption is there is an expectation that a large enough swath of the population will opt in whether they have been tested or not and whether they are asymptomatic or not to make it effective. Then if and when someone tests positive the data can be used to identify persons who were exposed to the carrier and have them tested and in turn test those they have been in contact with. Used in conjunction with accurate and effective tests, social distancing, voluntary or involuntary isolation, and hopefully at some point effective treatment this technique could have a major impact in flattening the curve. It is a tested and proven tactic in epidemiology.
As far as bluetooth range goes, newer devices are capable of ranges in the order of 100 feet maybe more. The wristbands at Walt Disney World are low power bluetooth and enable Disney to know where every person is within the parks as well as unlock resort doors, act as park and transportation passes, and pay for purchases. The batteries (if there are any) never need recharging. Whether the range can be modulated or not I don't know but location can be triangulated with far more accuracy than range modulation.
