I'd say that it depends on how the charm operates.
For charms that have an effect along the lines of "target believes caster is a good friend" (mental suggestion), I'd say no - you don't recognise "good friends" by metaphysical inspection, rather by appearance (first) and behavioural clues (second). Changing appearance would be a sure-way to be, in the target's eye, someone who is not his "good friend". In this case, the caster has "updated" the social patterns in the target's mind to associate his physical and behavioural clues with a positive reaction, and is thus tied to those clues.
For charms that have an effect along the lines of "caster appears as a good friend to target" (mental illusion), I'd say yes - the mental illusion is not linked to physical appearance or behavioural clues, rather by an internal mind landscape and the connection with the caster's mental identity. this would not change with the caster's appearance. In this case, the caster has overwritten the target's mind to appear to him as someone the target considers as a good friend, which is independent on the caster's appearance (since this appearance is rewritten in the target's mind).