When you go to tie in the battery source of power, consider adding a
switch to select between either the rectified power from the AC/DC
converter or battery power.
Alternately you can add two rectifying diodes that can handle the
current, ex. a 1N4001 diode. The rectifying diodes only allow current
flow in one direction. So without needing to throw a switch, power to
the speakers can come from the AC/DC or batteries. In this
configuration, the pair of diodes are referred to as ORing diodes.
If a switching method similar to one of the two mentioned above is not
done, there is risk of damaging the output of the existing AC/DC
rectifier *if* the rectification is done with a 3-terminal voltage
regulator such as the LM338. The LM338 has a low output impedance
(resistance). Current from the battery would flow to the speakers and
into the output of the LM338 and potentially damage the part.
Take a look and see if there is a 3-terminal device or just a resistor
and zener diode used for the rectifying. If it's just a resistor and
zener, then you'll just end up wasting a portion of the battery energy
in the zener.
Hopefully you can see better what I am talking about with the text
diagram "drawn" below. Anode-Cathode shows the connections of the
positive and negative sides of the diodes.
AC power-->AC/DC rectifier-->Anode-Cathode--\
\-->Regulator-->Speakers
/ (if any)
Battery power--------------->Anode-Cathode--/
Adding an switch or pair of rectifier diodes would require cutting the
existing connection between the AC/DC rectifier and the
regulator/speakers.