Nope. When the counter is at 0, and is told to count down again, it wraps around and starts at 15 again (Which is binary 1111)
The borrow pin is an output, that can be used when cascading more counters together... so what one counter hits 0, and is told to go down again, the borrow pin could make the next counter in the circuit count down.
The carry pin is the same thing, but will make the next counter count up when it's at 15 and told to go up again... without, it would go up to 15, overflow, and count 'up' to 0 again.
(Similar to how 80 becomes 79... the 10's position needs to decrease when the 1's position needs to count down below 0. The 1's position borrows from the 10's position)