No. A prime example of the examination of data at rest would be the execution of a search warrant, I do not view the execution of a search warrant as surveillance.
Your assertion that declining to view something as surveillance "bumps up against" something in the Constitution is baffling. Labeling something as surveillance makes no difference to its status under the 4th amendment.
If you actually believe that the NSA is peering into your storage devices to examine your data at rest, turn on your encryption. The remote rummaging through data at rest that you conjure would be cyber-burglary, not surveillance.
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