From a very old Tech Manual that I have for the -300.
The list of serviceable equipment when on Battery power only, is at the end of the Electrical section along with some diagrams.
It hasn't formatted very well bit this is a list of the navigation equipment that will be available to you.
Navigation
• ADF No. 1 • Captain’s RDMI • Captain’s HSI (non-EFIS airplanes) • First Officer’s RDMI (on some airplanes) • left IRS - AC • left & right IRS - DC (switched hot battery bus) • VHF NAV No. 1
My Tech. manual covers a number of a/c serial numbers, and diagrammatically it show that on some aeroplanes the ADF needle to be working, but the back card/RMI will not. I guess the answer to your original question is that it comes down to customer options.
The only other thing working on the F/Os side in this configuration is the clock, and on some models, the marker beacon lights!