Does total time exercising matter for cognition more than the time exercising continuously? Will my brain benefit from cardio equally if I exercise at the same intensity level for 12 10 minutes sessions as it would for one 120 minute session?
Before giving my gut feeling as an answer in the final paragraph I'll first have to explain why I don't think the question can be answered in absolute terms (at least not without additional restrictions).

To start with I'll remind you that our bodies don't just flick over to exercise mode but instead ramp up and down in response to the demands put on them. As a result to make a proper comparison between bursts and sustained exercise isn't as simple as multiplying there duration.

If we take our [calculated MHR][1] as a basic measure of exercise intensity then say a respectable level is 50% to 70% of MHR, the quickest we are going to be able to get into that heart rate zone is with an all out sprint (a very bad idea without warming up) at which point our heart rate will overshoot the mark (sometimes reaching well over 100% since the MHR calculators are pretty rough without doing a full fitness workup) and then drop and eventually settle on a rate after maybe 2 minutes. 

But the more likely and sensible scenario  is that we will start exercising at what we feel is the correct intensity and our heart rate will eventually increase over the space of several minutes so that it may be 5 to 10 minutes before we get in the zone.

So while I completely understand where you are coming from with your question it is one that I see a way of testing experimentally - and so i will just give you my subjective answer in what follows.

Since the physiological changes in the brain ([such as increased blood flow, seratonin, BDNF][2]) would I believe happen toward the start of the exercise session and then your brain would adapt to the new exercise demands and stop producing extras of all those goodies leaving them to begin dissipating before you ended the session and for a duration of time after means you would be better off doing bursts of exercise throughout the day to keep triggering that brain response that re-releases the goods.