I was recently sent a link to a research paper reviewing "Does Noise Affect Learning?" - reviewing research up to 2013 in the area.
Where the noise occurs when completing a task:
That acute noise exposure has a small but measurable effect on the ability to complete tasks effectively.
Auditory cognition is reduced with higher noise levels. This effect is progressively greater with younger children (12 and below)
Non-auditory tasks can be impaired by acute noise, again more so for younger children. 38% degradation of performance was measured for second graders.
That many modern classrooms (and homework study areas) do not provide sound insulation for ideal performance.
Where chronic noise levels impact on the overall performance of the child (through lack of sleep, hindered development or other longer term impacts):
In this area the research is less consistent, and many studies have not been well controlled. The best of the studies (controlling for Socioeconomic differences) concluded that Reading performance was measurably affected (for the worse) by the presence of Traffic or Aircraft noise in the home or school environment. Interestingly the study revealed enhanced performance in episodic memory with higher road traffic noise. The causality is unexplained.
Adult tests have demonstrated changes in the way the brain reacts to speech sounds in those with long-term exposure to occupational noise.
While the findings are not decisive, it is recommended that noise impacts be considered and mitigated for children due to potential long-term effects.