In other words, you can put any program in the buffer and then load it up.
No.

perhaps give you access to the command prompt or run some sort of process. Whether it has admin access depends on what runlevel the code is run at. So basically, if the program that you overflow only has limited access (XP terminology, I believe), you will not be able to spawn an admin account. The program has to have admin access in the first place.
Thats because you control the program so you'll be gaining whatever privileges set for it. Since almost every home user does everything with full administrative access it would never matter.