Q: Can I connect and boot PCIe SSD of MacBook Air Mid-2013 to another MacBook Air Early-2014?

Not likely. Since both systems have disparate hardware, hence drivers (e.g. display driver), they will not be compatible in that manner.

Try connecting the two systems via a Thunderbolt cable, and booting the "dead" system to Target Disk Mode. The other computer will then read the Target Disk Mode computer's drive, as it were a an external disk.

Or, you can alternatively reinstall the OS, using the "dead computer's" recovery partition to a blank external hard drive hooked up to the system, then use that installed drive to boot to, and gander at the internal drive, if it is any good.

If it won't power up, then you can't use Target Disk Mode.

If you don't intend to repair the unit, you may have to remove the SSD in order to simply read its contents.

macsales.com sells USB enclosures for MacBook Air SSD's.

http://eshop.macsales.com/item/OWC/MAU3ENPRPCI/