Should I 'run in' one disk of a new RAID 1 pair to decrease the chance of a similar failure time?
Solution 1:
It's a waste of time.
You won't be able to induce failure or stress the drives in a meaningful manner. You have RAID, and that's a good start. Just make sure you have monitoring in place to actually detect failures as they occur and backups to protect against disaster.
Solution 2:
It may be better to use different brands or series of disk together if you're worried about this.
I have seen disks of similar type and age fail in clusters, so IMHO it's not an urban leend.