Here is the situation:

1. Nightcrawler is carrying someone while using Hypersonic speed.
2. Nightcrawler moves adjacent to his target to attack them.
3. Nightcrawler hits.
4. Can Nightcrawler "drop" the character he was originally carrying adjacent to the hit character and then "pick up" the hit character to move it somewhere else?

No, the reason is that you can only place a carried character after you stop moving and when you attack with HSS, it happens during your movement. However, you can still take the hit character with you, not because it's being carried, but because Nightcrawler places a hit character after the action resolves.

The character is off the board for the entire action and is never actually 'dropped' until the end of the action.

Okay thanks for the help.