What is the purpose of halogen in oxidation of thiols?
Try drawing a mechanism without halogens present, starting with your base DE-protonating one thiol. See how far you get. The problem is that you'd have to somehow kick out H- (hydride), which is a terrible leaving group (enzymes can accomplish this, but standard lab reactions cannot do this easily). The fact is, combing two thiols to give the disulfide is an oxidation reaction, and there is an electron pair being lost from the reactants. It has to go somewhere, i.e. to reduce a diatomic halogen (playing the role of an oxidizing agent). 

The thiol-disulfide redox equilibrium you are asking about has great biological significance; see disulfide bridges (for protein structure) and glutathione (an antioxidant).