I have to wonder if it'd be possible to DDOS the NSA by having everyone do 'dd if=/dev/random of=supersecretstuff.txt count=1024 bs=1048576' and post large file

I have to wonder if it'd be possible to DDOS the NSA by having everyone do 'dd if=/dev/random of=supersecretstuff.txt count=1024 bs=1048576' and post large files full of random bits all over the web. The NSA would be obligated to collect and store every damn one of those huge blobs of random bits on the off chance it'd be used later as a one-time pad, or that it's encrypted secrets that they need to investigate. It costs nothing to generate random bits, but it costs > 0 to store that data. Sooner or later they'd just run out of disk space.