Can I run the EE1.14 Responsive theme in 1.13?
I am just trying to think things through and I think if I copy the entire package it should work?
SHORT: It will work with some tweaks/fixes.
LONG: It can certainly work. You'll need to fix a few things and make some tweaks but it's not that difficult. At CLS we've prototyped taking RWD as far back as 1.11 with pretty good success.
For our work, we've dropped RWD on top of whatever relevant version of Magento and then started fixing bugs as we went. Even going back as far as 1.11, in many cases you'll simply need to copy some new methods into core class overrides in app/code/local and things will work as expected. That won't be true for every issue, of course, but it will get you a long way down the road.
With a good debugger and diff tool you should be able to work through it pretty quickly. Especially going from 1.14 to 1.13 there weren't that many changes to frontend components other than RWD, so it should work out well for you.