Dual 4k displays on a Macbook Pro 15" Late 2013
In reference to your questions about setting up dual 4K displays...


  Will my MacBook be powerful enough to drive this dual 4k monitor
  setup?


No.  Your MacBook Pro is only capable of supporting 2560x1600 on two external displays.  In other words, it's capable of supporting dual QHD (Quad HD) monitors.


  Dual display and video mirroring: Simultaneously supports full native
  resolution on the built-in display and up to 2560 by 1600 pixels on up
  to two external displays, both at millions of colors


Source:  Apple MacBook Pro 2013 Technical Specifications

Additionally, this question/answer is very helpful in determining what displays can be connected and with what resolutions.


  Can I use MST and daisy chain the two displays from one thunderbolt
  port, or would I need to run a separate cable for each display?


You will need to run a separate cable for each display as  Apple, for whatever reason, chose not to support MST daisy chaining.


  Just generally will it work perfectly fine, or are there potential
  issues I should be aware of?


"Perfectly fine" is subjective, but assuming you connect a display independently to different Thunderbolt ports, it should work.  Additionally, it would be beneficial if you used a mDP (mini DisplayPort) to DisplayPort cable and not convert to HDMI.  If you must convert to HDMI, use an active adapter.