If you feed a different voltage into AREF you need to call analogReference(EXTERNAL); in
setup() before using the ADC, to prevent the internal linking of AREF to Vcc.
3.4V to 3.3V is a very small voltage drop, I would suggest just filtering the 3.4V heavily, rather than
expecting a linear regulator to perform well with 100mV of dropout. Perhaps RCRC filter to AREF.