Is there anything that forbids APU test when it's running? The answer is NO. Rather if you are not sure if the test was done you should do it.
Below from FCOM PRO NORM SOP
FIRE
APU FIRE pb-sw.......................................................... .........................................IN and GUARDED
AGENT lights ............................................................ ............................................................ ..... OUT
If the APU is already running, ensure that the following check has already been completed. If not,
perform it.
APU FIRE TEST pb.......................................................... ......................................................PRESS
Check :
‐ APU FIRE warning on ECAM + CRC + MASTER WARN light (if AC Power available).
‐ APU FIRE pb-sw lighted red.
‐ SQUIB light and DISCH light on