No.
If memory serves, a cow can be productive for 12 to 15 years. I'm sure I had several cows calving when they were well over 10. I don't think not calving for the first 6 years of her productive life should matter. While they can continue much longer, they start to slow down after about 10 years.
Our oldest cow (a fresian) got her last pregnancy at 13 years old.
We eventually removed her at 15yo, mostly due to arthritis that made hard for her to move around.
I have 2 heifers from the same cow and that cow was like 15 years old but she had something wrong with her digestive system and we had to get rid of her