If you just call, and BB calls:

The pot will be $2,185. The CO will be getting great pot odds on his hand when you push in your remaining $395 post-flop. If the flop comes K 9 4 rainbow can you fold to a bet from CO? If you fold, you have $395 remaining. If CO wins and BB is out, you're ITM but almost definitely 3rd. If you fold, CO loses, now you're the short stack, and almost done with only $395. If you call his bet (or he calls yours), you're getting 4.5:1 pot odds and you probably have the best hand. Just push pre-flop or fold. (I'd push).

If you and BB call, you have to push post-flop. Even if CO calls and beats you, you're something like 75% versus BB's random hand, so you'll still get third. So just push.

If you call and BB folds, then I could see folding post-flop to survive, but I still couldn't based on the pot odds I'm getting, and the fact that I'm probably the in the lead anyway.