I was wondering if it is possible to build an executable that does not require the use of an outside data folder.
This is not possible through Unity. You will have to use another program to pack the data folder and .exe file together and create a new .exe for you.
For example Smart Packer.
http://ludumdare.com/compo/2016/04/21/how-to-make-your-game-into-a-single-exe/
Follow the directions on this site, it teaches you in legit 2 steps how to do what your asking, it took me 30 seconds to understand, reply for any comments or concerns.
Sincerely,
VirtueRL