Now, I am taking it that you mean booting from something like a "thumb-drive"?
Unless there is something about the new version of Mandriva since they retooled their distro that I am unaware of, I can't see why you couldn't boot and run it from a USB device. As long as the hardware you are running on supports a USB boot, you should be able to do this fairly easily.
For long-term use, I wouldn't recommend doing this, since the constant accessing of the filesystem will run down the USB device *much* faster. Remember that those devices are generally rated on their MTBFs (Mean-Time Between Failures) by accesses (i.e. reads and/or writes). Many of those devices, especially the older ones, consider a read the same as a write. Newer ones are much more reliable as far as reads, but still have an MTBF based on writes.
If you are setting up a thumb-drive to be the root of your OS, I recommend compiling your kernel with CONFIG_BLK_DEV_PLATFORM. That is the linux kernel driver for using a "chip" (originally for Compact Flash chips) as a "true IDE" device. It's my understanding that it will help cut down 'unnecessary' accesses of the chip, though I haven't found any documentation yet to confirm that. Just the description of the driver within the menuconfig:
Code:
CONFIG_BLK_DEV_PLATFORM:
This is the platform IDE driver, used mostly for Memory Mapped
IDE devices, like Compact Flashes running in True IDE mode.
If unsure, say N.
Symbol: BLK_DEV_PLATFORM [=n]
Prompt: Platform driver for IDE interfaces
Defined at drivers/ide/Kconfig:244
Depends on: IDE
Location:
-> Device Drivers
-> ATA/ATAPI/MFM/RLL support (IDE [=y])
One last thought: Remember that for running persistently in linux, you will want a swap partition. You are going to have to separate that out on your USB device. There is an entire section of the linux kernel config dedicated to different types of flash-type chips and what you can do with them, including partitioning. Check them out. IIRC, you should find them under Device Drivers -> Memory Technology Device (MTD) support.
HTH.