It depends. When a SMART diagnostics tool like HD Tune Pro or smartctl tells you that there is a Current Pending Sector reallocation or an Offline Uncorrectable sector this might indicate a fixable sector.
To be clear, the data at that location on the disk is hosed. You're not getting it back. Sorry.
However if you use a tool to attempt to write to the faulty sector the drive one of two things might happen:
It will fail to write to the physical sector on the disk. The drive will then reallocate a spare sector from the drives small collection of spares. This is bad. Your drive will keep working for a while. As the people at Google found out when a drive start reallocating sectors it is not long for this world. This will show up as a non-zero Reallocated Sector Count SMART attribute value.
The write will succeed and subsequent reads will also succeed. Further examinations with a SMART diagnostic tool will show that the Current Pending Sector has decreased.
What's happened is that the drive will likely have experienced what the drive manufacturers refer to as a write splice. That is a sector which is incompletely written. These generally occur when power is removed from the drive when it is writing. Because the full sector hasn't been written correctly when the drive comes to read that sector it reports a read failure.
Some hard disk manufacturers diagnostic tools will fix up these write splices. For example Seagate's SeaTools for DOS (not the Windows version) will offer to fix drives after it completes a full long test. This avoid unnecessary RMAs for Seagate and may recover an otherwise healthy drive.