it was meant to make you aware of what was going on while you were out fighting... and it made sense, she's still connected to you soof course little bursts of her thoughts would come through, and since Gravemind had a hold of her, he had that same access...
but anyway, me and Soshi just finished it and i loved the ending!
click to show spoiler
i thought it was sweet when he said "Wake me when you need me", he was still a Spartan who was really tired... but he let Cortana know in his own way that he'd always be there for her! what! it could work! she's a computer, he's half computer! who else would want to deal with them?