Its a matter of economics, so yes and no.
The higher the precision of the machine, the more capable it is of holding the tolerance.
If the part is very simple, high dimensional accuracy is not too expensive because the unit cost of the reject units is low. It usually takes a few units to get the tooling set right, and the
program adjusted, etc.
If the material is easy on the tools, then you can expect quite a sustained period of accurate production. That is, if you can predict the performance of your machine spindle as it warms up during the run.
If the material is tougher on the tools, then you've usually got to endure a cycle life on the tools, and it sometimes takes quite a number of units to determine what the typical tool life is. This will include frequent gaging to observe the evolution of the tool wear. Whenever a new tool is substituted for a worn one, the cutting action can be markedly different while the new tool "breaks in", then settles into its "typical performance" for the rest of its wear life.
A good quality machine is very repeatable so far as its own positioning is concerned, but how tools behave is like running a new experiment for every program, and every tool.