In series (with a battery I assume) the resistor would affect the timing of the charging of the capacitor, but not the end result. The capacitor would eventually become fully charged, the current would fall to zero, and the resistor would be irrelevant (no current means no voltage drop).
In a parallel system with a battery, yes indeed the two electronic objects would behave independently. The battery itself would see a difference in amount of current coming out of the battery, but the capacitor behavior would not take the parallel resistor into account; it would behave the same if there was no parallel resistor.
