Yes, you wouldn't be able to measure it accurately, but it's nonetheless a static amount of time unrelated to the Earth's orbital period.
I'm not an astrophysicist, but I'd guess the Earth's orbital period isn't quite the same as when the planet first formed either. So using today's defined measurement of "years", the planet's age and the number of times it's been around the sun might not match up at the surface either. The impact that formed the moon must have changed our velocity a bit, right? And the sun has been losing mass (into energy via fusion) since it first formed.