Even a small tear means your fridge is pulling in warm air from outside, and yeah, it's going to compensate by running more often. The compressor cycles harder to keep things cold, which burns extra energy and puts unnecessary strain on the system over time. Food near that door also won't stay as cold as it should, so you might have spoilage issues creeping up gradually.
The good news is you don't need to rush like it's an emergency, but I wouldn't sit on it for months either. If the tear is small and isolated, you've probably got a few weeks before it becomes a real problem. Grab a replacement gasket for your specific Samsung model - they're cheap and yes, super easy to swap yourself. Just pull the old one out and press the new one in around the door frame. If you're not feeling it, any repair tech can do it in minutes for not much money. Better to just get it done sooner than later and stop wasting money on extra energy costs.