Probably not. In 90% of cases, that puddle is caused by a tiny, often overlooked component:
It drips down a channel, through a small hole (usually located on the back wall inside the fridge, just above the bottom shelf), and travels through a tube to a drain pan underneath the appliance. Once there, the room temperature air evaporates the water away.
Here is everything you need to know about why it clogs, how to fix it, and how to prevent it from happening again. Every frost-free refrigerator has a defrost cycle. Several times a day, the fridge warms up its cooling coils just enough to melt any frost. That melted water (condensation) has to go somewhere.
If you see ice covering the hole, do not chip at it with a screwdriver (you can puncture the plastic lining). Instead, use a hair dryer on low heat held 6 inches away, or press a towel soaked in hot water against the ice until it melts.
Mix 1 tablespoon of baking soda with 1 cup of hot (not boiling) water. Use the turkey baster to squirt this mixture directly into the drain hole. If the water flows down and disappears, you are done!