You'll do as well or BETTER by buying either a USB3 enclosure, or just get something like this handy little device: There aren't many external thunderbolt enclosures 'out there' to buy. 'If there's no NVMe slot then I'm just going to rock an external SATA SSD. If this machine was purchased without an NVMe drive - if I open it up will the slot for NVMe still be there?' The Late 2015 got rid of the SSD slot if you got a HDD only config. The Late 2013 and Mid 2014 should have the SSD slot even with a HDD as the configured option. I don't believe Apple started changing this until the 2015 models. The SSD slot will be there, whether or not he configured with SSD or Fusion. The Late 2014 Mac mini also supports NVMe drives. You must upgrade to at least 10.3.2 for booting from NVMe to be considered stable. The earliest machine that I have personally tested in the Late 2013 Mac Pro.

I haven't personally tested in the iMac, but my understanding is that you cannot boot from it in a Late 2013 model. The Mac did not gain support for NVMe SSDs until the 2014 model refreshes. IFixit shows that you should have the SSD slot available. Not to mention, you keep all of your USB ports available. If you were to put an Apple OEM SSUAX 1TB PCIe SSD, you will easily get three times the speed.

This is recommended WAY TOO much around these forums.

Late 2013 imac 27 upgrade memory