Random Movement and Characters

The Random Movement special rule as such does not preclude a character from joining a RM unit, provided there are no other factors that him prohibit from joining. The BRB does not specifically address how such a combined unit would move, but BRB p. 74 specifies: "If two or more models in a unit have the Random Movement special rule, pivot the unit about its centre, then roll the dice only once to determine how for the unit moves. If models in the unit have a different Random Movement value, use the slowest for the entire unit." So, if there are at least two RM models, the combined unit would always follow the RM special rule. 

If the character would join a single RM model, then BRB p. 99 comes into play: "A unit always moves at the same rate as the slowest model, so when the unit moves, charges, flees or pursues, always use the lowest Movement characteristic and rules of the slowest troop type. Similarly, if the character is subject to any movement restrictions, then those restrictions apply to whole combined unit whilst the character remains part of it, and vice versa" (Italics mine). The problem here is that the RM characteristic is..well..random, and we do not know a priori which model would be the slowest. There are a number of options (including simply not joining), and you should discuss this with your opponent. Rolling the RM distance first is problematic, since you pivot the unit before rolling, and thus have already made your choice. Perhaps the most practical is either to always use the RM characteristic, or to take the lowest possible RM outcome when determining the slowest model. So, 2D6" would equal 2."