Yes. Watch the water drip. If you got all of the old packing out it is recommended that your put 3 pieces in. The smaller size and 3 circles will provide a better seal. Be sure to follow the instructions.
Cut 3 rings the diameter of the shaft.
Make the cut on a 45º angle
The length of the piece should be so there is a little pressure holding the cuts together.
stagger the cut lines so they are not on top of each other at about 120º apart
Close the stuffing box beyond snug tighten when in the water so water stops when no shaft rotation but drips when rotating.
To keep the shaft and stuffing box just warm to the touch.
MaineSail has a great article on the stuffing box. Can be found here.
Re-Packing A Traditional Stuffing Box - Marine How To
This thought describes what you are trying to achieve.
"If a stuffing box is allowed to drip, even at a slow rate, it allows for excellent cooling, longer shaft life, less opportunity for crevice corrosion and less opportunity for trapped air to run the box in a totally dry state and cook it. (MaineSail)"
