Prevent battery from getting charge
Yes, it could work for you. Be advised that the +12v Constant input will draw current from whatever voltage source is higher.
I think it is quite likely that you really don't need +12V at the Constant input. I would see if your settings are remembered if you apply, say, only +9V at that input. In that case you could use a lower voltage battery pack and that would ensure that power would always be drawn from the 12V supply when it was connected and turned on.
I would also measure the amount of current that the +12V Constant input draws. It's likely to be very small. The diodes will reduce the voltage reaching the +12V Constant input, but if the current draw is small the voltage drop will also be very small.
(btw, the battery symbol in your schematic is the wrong way around.)