Not without manual modifications. Also note that there is not really an "RPi desktop OS" but it is a regular Debian with the RPi repository added which allows to install (and ships pre-installed) the modified LXDE, but the desktop is purged by PREP, so it doesn't make much sense to use it as basis for PREP. And the main issue still is that the bootloader is overwritten .
But actually, is there an issue with the DietPi-controlled grub as bootloader? As said, PREP installs os-prober temporarily before creating the grub config so any other OS should be selectable from the grub menu at boot. I'm not 100% sure whether this is kept when grub is upgraded later, I guess you need to install again the os-prober package for that and keep it installed.
And also then grub should be uninstalled on AntiX so that there are no two grub packages which flash the bootloader back and forth. Or remove it from DietPi so that it is controlled by AntiX only.
Long-term we'd need a non-bootloader DietPi image, containing a singe partition only and no partition table so that it keeps bootloader and existing partitions in place .
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