Does voltage drop on power cable depend on the type of MCB used
(note: this answer is based on UK knowlage, I expect things will be similar across Europe, the USA has it's own standards which are very different from the European ones)

Volt drop in the cable depends only on the cable, there may be some volt drop in the MCB itself but I would expect it to be negligible. I've certainly never heard of anyone using it in design calculations.

However volt drop is not the only factor (or even the most important factor) in choosing a cable. There are three factors that need to be considered.


Cable rating, will the cable overheat due to either normal load or overloading.
Volt drop, will the resistance of the cable result in unacceptable volt drop at the load.
Disconnect times. Will short circuits be disconnected in a timely manner.


Point 3 is where there can be a relationship between breaker type and cable length. To ensure short circuits are disconnected in a timely manner the short circuit current must be sufficiently high. 

In particular MCBs are hybrid devices, they have a thermal section for disconnecting overloads and a magnetic section for disconnecting short circuits. To ensure fast disconnection you generally need your short circuit current to be high enough to hit the magnetic part of the breaker.

For a type B breaker your short circuit current needs to be at least 5 times the breaker rating to reliably trigger that magnetic trip, for a type C breaker your short circuit current needs to be at least 10 times the breaker rating to reliably trigger the magnetic trip and for a type D breaker your short circuit current needs to be at least 20 times the breaker rating to reliably trigger the magnetic trip.

(type A breakers don't seem to exist)