I know that, as a cloaked spy, I can recharge my watch from a dispenser. In fact, a L3 dispenser can recharge my watch faster than it drains. However, I know that dispensers display a glowing tether to units that they are resupplying. If I cloak next to (or on top of) an enemy dispenser, will I get tethered and thus be revealed to detail-oriented Engies and Pyros?
No, cloaked spies will not be tethered by dispensers. Most special effects are hidden while cloaked, with notable exceptions being milk/jarate/blood/water drips and fire.