Can cognitive enhancement from exercise be replicated/replaced through prolonged standing?
Like, will BDNF be released from prolonged standing. I would prefer to use a standing desk than exercise (due to wanting to save time).
Slightly longer answer
This fairly recent review shows little positive effect of standing desks and mixed results of treadmill desks for cognitive outcomes (note: this is a summary of 23 full studies). Only treadmill desks were actually studied for cognitive performance, and even those showed no effects.
There were some positive physiological outcomes for both standing and treadmill desks, but much more consistent with the treadmill desks. The treadmill desks seemed good for weight loss, though, especially in obese participants.
All in all, it doesn't seem like a mere standing desk is known to give direct cognitive benefits, though the existing studies are all fairly small. It probably won't hurt, although standing for long periods can be problematic, too.
None of these studies compared the effects of the standing desks to the effects of exercise.
MacEwen, B. T., MacDonald, D. J., & Burr, J. F. (2015). A systematic review of standing and treadmill desks in the workplace. Preventive medicine, 70, 50-58.
There are studies, however, like this one:
Mehta, R. K., Shortz, A. E., & Benden, M. E. (2015). Standing up for learning: A pilot investigation on the neurocognitive benefits of stand-biased school desks. International journal of environmental research and public health, 13(1), 59.
...that purport cognitive benefits of standing desks. However, it is important to note that one of the authors has patents on standing desks that are licensed by companies that produce them, including some of the desks used in the study.