Nsgarch
1. Balanced cables are only "quieter" if carrying a balanced signal (a plus and a minus referenced to a neutral conductor) in which case noise in the normal (non-inverted) signal cancels with the noise in the inverted signal -- this is known as common mode rejection. So if, via an adaptor, one sends a single ended signal ONLY (in other words, half of a balanced signal) through a balanced cable, common mode rejection doesn't come into play. So there goes the noise rejection advantage.
I'm afraid that's incorrect.
Balanced interfaces and the common-mode rejection that they offer have nothing to do with the signal. A balanced interface rejects common-mode noise even when there is no signal present, and it doesn't matter whether the signal's being sent asymmetrically on one line, or symmetrically between both lines.
What "balanced" refers to is the impedance of each line with respect to ground. The source impedances must be balanced in order for the differential input to be most effective at rejecting common-mode noise. Any imbalance will degrade this rejection.