Would a charged capacitor react differently to a continuity test than a discharged?
Yes, but with caps that small it should not make a difference.  Generally your meter measures continuity by applying a small current and then measuring the voltage drop.  A short circuit will produce a very small voltage drop.  If you connect a large capacitor that's discharged, this current will charge up the cap.  As a result, it might take a while for the voltage on the cap to rise above the 'short circuit' threshold, so the meter may read the cap as a short circuit for some time while the cap charges up.  This will only be noticeable if your cap is at least 100 uF or so.  If the cap is already charged, then the meter might just read the cap as 'open'.  However, I would be careful about measuring large charged capacitors in continuity check mode as it is possible that they could damage the meter and/or give you a nice shock.  With caps smaller than 1 uF, it won't make much difference, and they were probably already discharged by the circuit anyway.