No, there shouldn't be any need for a RW filesystem, though the launcher script will/does(I forget if it's in the latest, or just the version I'm working on) include a tarball of script files which get extracted at runtime. Obviously, provided that those script files are in place when BackupMenu.item gets run, everything will be fine.

Oh, there -are- a couple of files in /tmp/ that get written too(status files) - You'd want to mount a tmpfs there before running BackupMenu.item
Note that that's not hard, and tmpfs support -does- seem to be compiled in.