Generally no, especially with a toroid, but you must be careful with positioning the transformer in relation to sensitive electronic circuits. In extreme cases I have wrapped a shorted turn of copper or aluminum sheet around the outside of transformers to reduce hum.
This approach is not unusual in commercial amps, especially pre amps. Don't confuse an external shorted turn with an actual shorted turn, which must be avoided or the transformer will be wrecked. It is very easy to accidentally make an actual shorted turn with a torroid, so watch for this when mounting a toroid. A conductive mounting bolt thru the center of a toroid can cause an actual shorted turn. One case I came across was an amp that was growling: someone had fitted to long a bolt in the center of a toroid and generated a shorted turn. The bolt was quite hot.