Effect of length on a thermocouple's accuracy

There's no significant voltage drop because there's no significant current flowing - thermocouple amplifiers have a very high input impedance.
You also need to remember that a thermocouple sensor does not generate a voltage at the sensing junction - the voltages are generated along the length of the wires and the voltage generated along each wire depends on the temperature difference from one end of the wire to the other (from sense junction to thermocouple amp).
Because each wire is made from a different material, the voltage generated is different even though the length is the same, and the thermocouple amp measure the difference between these 2 voltages.

Wire cable resistance is insignificant when compared to the input impedance of the amplifier which is so high that the wire doesn't affect the measurement.

For example, the LT1052 (which would be great for a thermocouple) has a 30pA input bias current, which corresponds to over 100MΩ of resistance. Wire cable even in the 100Ω range with a 30pA current would be about 3nV of error.

What does cause greater problems are temperature effects from other thermocouples, such as the connectors to the board and the thermocouple junctions formed between the pins of the opamp IC and the PCB. It is necessary to make sure that the connector is thermocouple effects are matched to reduce error.

Another problem is the voltage offset of the op amp, because themocouple voltages are in the mV range, voltage offsets contribute to error, so look for a low voltage offset (and one that doesn't change with the temperature of the op amp much)

Thermocouples used for temperature measurement don't suffer much voltage drop because the thermocouple interface electronics don't draw any current from the thermocouple (ideally, they don't draw any at all).

You may have problems with other effects, but voltage drop should be negligible.