Knightfall
World of Kulan DM
No, while Tim wouldn't be threatened, the characters are rushing with some urgency. It's not a casual climb up to the top. And, only the part where you're climbing has to be at 1/2 speed. It doesn't affect the rest of the movement other than you can't climb while using the withdraw action.
Since Tim would only have 15 feet worth of movement left when he reaches the ladder, he can climb at 1/2 speed and need only roll 10 or higher. This would put him 7-1/2 feet up, probably rounded down to 5 feet. So his feet would be just above Akos and Maggs' heads.
If you want him to reach the full 15 feet up the ladder it is a roll and the DC is 25. Since Tim is a Large character and the walls are only 10 feet apart, I'll say Tim can brace himself on the walls as he climbs. This gives him a +5 to his roll.
