False. Detectable is an experimental limitation of a given measurement system. Even one single virion can infect a host.
Think of it like chemistry. Sure, two covalently bonded hydrogen atoms at STP could have nuclei 1cm from each other due to random chance. However, the probability of this happening is so low that it is effectively 0.
If one bounds the risk from HIV from an undetectable partner to an unmeasurably small epsilon, dwarfed by other risks by many orders of magnitude--- the edges where the assertion are false don't matter.