A lot depends on your definition of what constitutes 'a break'. Many are likely to argue a break involves relaxing, a 'fun' pastime, which in another question on this site has been discussed to be beneficial for the work environment in the case of social activities:
..., having fun at work was perceived to positively
influence workplace relationships to a moderate-high degree,
contribute to managing stress to a moderate degree, improved job
satisfaction to moderate degree and was reported to have a little more
than neutral, direct impact on workplace effectiveness. These outcomes
must however be examined in the context of results, suggesting not
only are different types of fun activities enjoyed more, but different
types of activities are highly salient in relation to the particular
organisational variable measured.
However, these results do not seem to generalize to your scenario, as you seem to be more interested in taking a break from ongoing work and potentially switching to other mentally demanding individual work.
Therefore I believe the following study on multitasking—the interleaving of several primary tasks—which are
executed one at a time) by Adler and Benbunan-Fich (2012) measures results more in line with what you are after.
Our results show an inverted-U pattern for performance efficiency
(productivity) and a decreasing line for performance effectiveness
There is thus an optimal amount of task switching which leads to the highest productivity. However, increased levels of multitasking lead to a significant loss in accuracy, indicating a trade-off between productivity and accuracy.
These results thus seem to confirm that in at least the context of the study switching to a different task can improve productivity, in line with increased effectiveness when taking 'a break'. To which degree (and if at all), however, will depend highly on the specific tasks and work environment. For example, a follow-up study by the same authors (Adler and Benbunan-Fich, 2015) shows that subjective task difficulty is a determining factor: easy tasks
benefit from multitasking by increasing stimulation, whereas hard
tasks decrease performance as the result of an overload in mental
Adler, R. F., & Benbunan-Fich, R. (2012). Juggling on a high wire: Multitasking effects on performance. International Journal of Human-Computer Studies, 70(2), 156-168.
Adler, R. F., & Benbunan-Fich, R. (2015). The effects of task difficulty and multitasking on performance. Interacting with Computers, 27(4), 430-439.