I do not think the results of the experiment mean what you think they do

Messy Room 

Why a Messy Workspace Undermines Your Persistence
[Via HarvardBusiness.org]

Clutter makes you a quitter.

[More]

They put students in a clean office space or a messy office space.

They then did this:

Then, in a separate room, they were asked to undertake what was described as a “challenging” — actually, it was unsolvable — task that consisted of tracing a geometric figure without retracing any lines or lifting the pencil from the paper. Those who had been exposed to the neat environment stuck with the task for an average of 1,117 seconds before giving up, more than 1.5 times as long as those who had been exposed to the messy space (669 seconds). 

Their conclusion – the messy room depleted their mental resources so that they were able to persist with the task for much less time than those exposed to the clean room.

Or it might be that the messy room people were able to see the unsolvable nature of the task sooner and just stopped.

Giving someone an impossible task and then feeling that those who keep at it longer than others are doing better seems to not be sustained by the evidence.

Especially since other research has shown that creativity is enhanced in messy environments.