Why would it? The SIM card itself has no real functionality, and cannot just randomly affect the radio components of the phone. It just stores its identity and keys, so the cell tower can identify and bill the right user.

The way the location tracking works is simply by logging what phone connected to the cell tower, at the tower itself. To be able to adjust the power the radio component needs to output (to get a good signal), it needs to know the distance to the tower. You get location by then correlating with multiple towers, because the phone has to choose which one it has the strongest reception to, and therefore has to gather data from all nearby towers.

In short: that’s not how a SIM card works.