The cabinet of the president consists of the following positions:
Secretary of State
Secretary of the Treasury
Secretary of Defense
Secretary of the Interior
Secretary of Agriculture
Secretary of Commerce
Secretary of Labor
Secretary of Health and Human Services
Secretary of Housing and Urban Development
Secretary of Transportation
Secretary of Energy
Secretary of Education
Secretary of Veterans Affairs
Secretary of Homeland Security
Each of these positions, except Vice President, is also responsible for managing the department which reports up to them, something Snowden certainly lacks the qualifications to perform. At best, Snowden might have some qualification to serve as the Secretary of Homeland Security but there's still the management level experience that he lacks and he would never receive a confirmation from the Senate anyway.
The only non-confirmation positions that Snowden could be in that are in the Cabinet or are equivalent to Cabinet positions are the Vice President and White House Chief of Staff. Since Ms. Stein hasn't said she would make Snowden her running mate that's out of the picture, and I doubt he has the skills necessary to perform in the role of White House Chief of Staff.
Ms. Stein's statement on putting Snowden on her Cabinet is blatant pandering for votes. Nothing more, nothing less.