Answer:
It's impossible.
First of all,
CO1 and ST tell us that the vertical side of the rectangle is of size at least 4.
Second,
AI, ER, IR and CO2 tell us that the other side is of size at least 4 as well. Therefore we are aiming at a 4x4 square.
Finally:
Just before you move the CO1 up
(you clearly have to at some point)
$\bullet$ you need to have moved the other O to the left before that (there is not enough room on the right) otherwise you break the no two identical letters adjacent rule.
$\bullet$ you also need to have moved IR to the left (to make room for the CO1 to move up).
$\bullet$ you cannot possibly have moved ES up, otherwise moving CO1 would result in disconnecting ST from the rest of the board.
Conclusion: at that very moment, the block CO1 ST ES is disconnected from the other letters.