Adoption of any or all of the NFHS's suggested speed up rules is up to each state association, so it would depend on whether your state has adopted them and whether its rule is more specific than the suggested rule, which doesn't discuss this issue.
In my state, the rule is used, but the state high school association web site doesn't have any information on its web site.
Pitcher is defined in rule 2 as the player designated in the lineup as being responsible for delivering the ball to the batter. Catcher is also defined but not in a way that sheds light on this question.
Since the a) the proposed speed up rule doesn't specify that the pitcher or catcher must have previously pitched or caught, b) the only potentially relevant definition refers to designation within the line up, and c) the presumed purpose of the courtesy runner is to have next inning's pitcher and catcher ready to begin warmups properly, I wouldn't have any problem with an announced legal substitute for the catcher being lifted for a courtesy runner before he has actually caught.
I would ask the people telling you otherwise to cite their authority.