Very Unlikely
When the public was first learning about Snowden (and what he did) in the summer of 2013, the quote was attributed to "anonymous" or unknown. Given the topicality, Snowden was often mentioned in threads about the quote, and even used as a background image for the quote, but not in a way that suggests attribution. It was only later that people began to credit him directly for the quote.
A timeline, with facts about Snowden from Wikipedia:
- Summer 2012: Snowden starts illegal downloads
- January 2013: He makes contact with a documentary filmmaker
- February/April 2013: He starts working with a journalist at the Guardian
- May 2013: He claims medical leave and flees the US
- June 9, 2013: The Guardian reveals Snowden's identity at his request
- June 14, 2013: Criminal complaint filed against Snowden
- July 11, 2013: First (known) Twitter posts with the quote. There are several more examples on Twitter within the month, all listed on Barry Popik's blog.
- July 27, 2013: First (known) example on Reddit
- August 3, 2013: Quote hits it big on Reddit (multiple times) and Imgur. The presentation of the meme was slammed on Reddit, while other comments also made fun of the attribution to "anonymous" and instead wryly attributed it to the meme-quote-fabricating section of the internet (and therefore nobody important). It's not conclusive proof, but it does show how the quote was perceived at the time.
None of these social media posts attributes it to Snowden. As a conclusion, I agree with Barry Popik:
The saying is often credited to American whistleblower Edward Snowden, but Snowden’s quotations have been widely reported in the media and this one does not appear in any direct citation.