Only at a very few specific banks. It has been possible in the past to deposit from prepaid CCs, through a Walmart Money Center, to Bluebird and/or Serve cards from Amex the bank. (Those are considered "banking alternative" cards rather than a bank per se). That has been shut down to large part because people were using it like there's no tomorrow for Manufactured Spending, and both Amex and Walmart got tired of it.

As mentioned above, to get good solutions you need to mention your specific bank (since what's available varies widely from bank to bank) and also about how much money you're talking about (ie, the solutions for $10 are completely different than the solutions for $100000).