No, not at all.
The water line to it? Well, yes, that you DO have to worry about.
The poly tubing that comes with the fridge? Throw it out.
It’s easy to damage, and gets brittle when old.
A better choice would be “anything else”. That includes copper, braided plastic, braided stainless steel.
Is this a big deal? Yes. Water damage is a big deal, because of how much the repairs cost. The supply line is only 1/4 inch, so you won’t hear splashing water. And because the line is out of sight, the leak could last for a long time before detection.
Saddle valves get their name from the way they are clamped to the water pipe from both sides. You know, like a saddle.
They are not allowed according to plumbing code because they’re prone to leak. (They don’t always leak, so there’s that.)
The helpful folks at Handyman Magazine have a great article on how to replace the valve and line.