In theory you can get data off a hard disk that has been overwritten. You can see the faint traces of the magnetic fields from the previous data writes and try to deduce information from tat.
In this case though someone says the CVR is solid-state so different technology.
SSDs are actually easier to recover erased data from than magnetic based drives, a little appreciated truth. However, because of the way that consumer SSDs are designed this recovered data tends to be less contiguous making it more difficult to extract coherent information. Overall, I wouldn't be optimistic but if they pass the CVR along to the NSA I wouldn't be entirely pessimistic about their chances either. I'm sure they would find it a nice challenge.