That's right, here we are with the official draft order of the EoFFFFL... Counting down from the last pick to the first, here's what we've got:

14. Viewtiful Smiths
13. Los Angeles Enforcers
12. The Wizards
11. JimmyJimmy DumDum
10. Cincinnati Dragons
9. Vick's Best in Show
8. Vermont Greenscums
7. Midnight Ramblers
6. edczxcvbnm's Angels
5. The Burning Legion
4. Los Banditos
3. Free Bacon
2. Valley Fever

Which means the #1 overall pick in the draft goes to Defending 3rd Champ! Using my patented superfair psuedo-lottery system, the #1 pick was actually floatin' around until the next-to-last draw.

And yeah, it is possible as long as two teams have a working agreement on who drafts who. You can make the trade as soon as the draft is over.