Yes. In the tenth mission, You and Emile are delivering the Package to the Pillar of Autumn, but en-route to going there, a scarab stands directly in your way. Carter,, wounded and in a burning pelican, has this conversation with you as he dies --
"A Scarab suddenly walks down in front of Emile and Six.
Emile-A239: "Mother... We can get past it, sir!"
Emile walks back in hesitation.
Carter-A259 (COM): "No you can't. Not without help."
Emile-A239: "Commander, you don't have the firepower!"
After noticing the two Spartans, the Scarab charges its main cannon, aiming at the two SPARTAN-IIIs. Carter's Pelican flies over and shoots at it. The Scarab is distracted and stops charging its cannon.
Carter-A259 (COM): "I've got the mass."
Emile-A239: "Solid copy. Hit 'em hard, boss."
Carter-A259 (COM): "You're on your own, Noble... Carter out."
Carter rams the Pelican into the Scarab's side as it charges its main cannon again. The Scarab's side bursts into flames, explosions rocking within it. The Scarab lets out a dying scream and struggles to stay on the cliff. More explosions rock it and it falls down the cliff. A loud explosion is heard indicating its destruction. The view switches back to the two SPARTAN-IIIs."
It is fantasized that Carter could've jumped out just as the Pelican hit the Scarab, but as he says carter out, less than half a second passes between him finishing his sentence and him crashing into the Scarab. He couldn't have survived, and this is how he dies.