The cold junction is formed at the point where the thermocouple wires are joined to a dissimilar metal. In most cases, this is at the terminal strip of the AD module that reads the voltage and converts it to temperature. In high accuracy systems, the terminals temperature will be measured by a sensor located on a metal block with the terminals, forming what is known as an isothermal block and is often either copper or aluminum. The sensor is often either an RTD or thermistor. The terminals are electrically isolated from the isothermal block but are physically attached so that all are at the same temperature as the compensating sensor. Any difference between the actual cold junction temp and the measured temp is directly reflected in the reported temperature.
There are many ICs on the market where the cold junction compensation is part of the chip. The data sheets fro these invariably recommend that the board layout place the cold junction as close to the chip as possible to reduce the compensation error. This requires that the leads going directly to the board match the thermocouple being measured. This is obviously impossible where more than one thermocouple type is possible and where it is impossible to terminate the thermocouple directly on the board. In this case, accuracy depends on the temp of the chip and the temp of the terminal forming the cold junction remaining fairly close and stable.
Enclosing the PLC to stabilize its environment will probably help, especially if the operating environment is otherwise subject to wide fluctuations. If you have a couple of spare channels, the cold junction compensation can be measured by shorting a channel with a piece of copper wire, the reported temp will then be the cold junction temp that is being used. Connecting a very short thermocouple to another channel will give some idea of what the true cold junction temperature is. It is also possible for the cold junction sensor calibration to be wrong.
It's important that the path from the hot junction consists only of high quality thermocouple wire or extension wire, matching the thermocople. Any splices must be either with proper hardware made of the appropriate metals, by very tightly twisting the wires together or by welding so that no false junctions are formed.
The short answer your original question is yes, on many different systems. As a general rule, I expect about ten times the accuracy from an RTD as I can get easily from thermocouple because of the problems of cold junction compensation.