Yes, the inherent balancing helps reject power line (and other) uniform induced current. The twisted pair must end in a transformer or a circuit that can reject the induced current. Transformers are also an easy way to isolate the cable wires from external voltage sources (e.g., a short from the power line running across it) or common ground loops between equipment.
Once upon a time I was asked to evaluate a twisted pair networking system (before Ethernet was real widespread) before it was adopted as a company product. It did not work very well and I warned them that the cable conductors were not isolated from equipment ground. They ignored everything I said, and started buying them. They took my test system over to manufacturing and they set it up in their lab. Worked as well (badly) as it had for me) and then they added one new station. They blew/burned holes through every network card in the system and trashed many of the PC mother boards. The last PC was plugged into an outlet that was connected to a different distribution power transformer. Ground voltage difference caused hundred of amps to flow. This is why you have to be real careful about knowing how grounds really behave. You usually don't run into this in residential because code specifies only one earth ground and everything is usually coming from a single transformer. But in commercial and industrial settings this can happen if they are not careful.
The twist helps to cancel the induced current between adjacent twisted pairs. This characteristic is why the twisted pair works so well at high frequencies with multiple signals in the same cable. Twists are a function of the wavelength of the signals for which the cable is designed. If you look closley at cat 5 you will see that each pair is a different rate of twist. This is to enhance the cancellation between pairs.
The regularity and tightness of the twist and the orientation of the pairs is extremely important to high frequency performance. That is why you should never stretch (hey Bob, its stuck, pull harder), pinch (e.g., staple improperly), or bend below a prescribed radius for twisted pair or coax. Much of the signal deterioration in things like cat 5 occurs where the pairs are untwisted to install connectors. You have to untwist the absolute minimum amount of wire and use the shortest possible lengths to get to the connector. It really matters. These points may not be well recognized by everyone string the "low voltage stuff".
If you abuse the cat 5, it may work at 100 Mbps, but not well at 1000 Mbps. Ideally you should test all cables before you close everything up for frequency response and continuity.