Is it possible to boot from the software mirror?

Rumor is it is not possible to boot an operating system from the software array. Not exactly.
All of the modern boot loaders, ones coming from NT, Linux LILO, and GRUB, would happily boot from a RAID 1 (mirror).
It should be noted that some additional measures should be done to achieve boot redundancy if you are going to build a RAID. Since the mirroring does not cover the Master Boot Record, you should copy the MBR sector manually between hard disks in software mirror. If you omit the above, then
when the primary (boot) drive dies, you are left with an unbootable system.

Surely there will be no irreversible loss of data - all you need is to just attach the good hard drive into a working PC and read it, but no automatic recovery is possible if the drive stops working in operation, requiring a reboot.

Make a software RAID bootable?

Is it possible to create a bootable software RAID0, RAID 5, or JBOD?
The answer is "no". It is impossible to start an operating system off a software RAID0, RAID 5, or JBOD.

A hardware controller is required to be able to to make a RAID bootable. You cannot start an operating system from the software RAID because the RAID is not readable until the operating system is done loading, and the operating system itself is on the RAID.

Your only option is to start an operating system using a software RAID 1. To boot from a "second" drive of a software RAID1, one may need to copy the master boot record first, because typically the master boot record would not be subjected to mirroring.