SMART self test doesn't reallocate anything. In fact, it stops immediately on first error. And (at least on modern Seagate disks) it starts with testing known bad sectors and usually stops there.
The rules are simple. If you try to read a bad sector, the disk will retry many times (anywhere from a fraction of a second to many seconds, maybe minutes), then return an error if it still can't get good data from it. If a bad sector is luckily recovered on read, or if its contents are replaced by a write, the disk will try to write the sector and read it back. If that works out OK, it will consider it repaired. If it doesn't, the sector will be reallocated to spare area.
If you don't care about the data currently there, you can simply continue using the disk as if nothing happened. If you continue having problems with reading back newly written data, you know the disk is not reliable. But you already have problems, so you know it anyway. That being said, such disk may still be useful if you have other copies of the data.
You can test a disk by writing it from start to end and reading back. This should also reset the "Current Pending Sector" count to zero, and it may or may not increase "Reallocated Sector Count".
What I've done many times is to map the bad sectors, then make the partitions skipping the bad area plus a margin of 1gig, some drives worked for years without issues, but never rely on that drive for anything important!
This makes sense for localized damage, and I have done it once for a friend. Last time I heard, the disk was still in service after several years. But it won't help if you have random errors in random places due to some mechanical or electronic problem. Particularly, if a disk keeps creating bad sectors and then repairing them by simple overwriting without reallocation, and then creating new bad sectors elsewhere, you just know not to expect much from it.