Yes, but only in special laboratories. You see, even if the harddrive has physically replaced 'secret data' with zeroes, there are still residual tracks on the physical medium that could identify the previous contents.
Such an attempt would be difficult at least, and impossible for people without access to high-profile laboratory equipment, though government agencies like NSA might be able to do it.
That's why the US DoD (Department of Defense) requires data to be destroyed by writing random junk data (not zeroes) to the medium for up to 29 times. This would ensure that no physical recovery is possible with the technologies we have today.