i had done something similar, but it required the phone to be switched off for booting the desktop linux as mbr on n9 did that, and so the entire N9 mmc had to be exported to the pc.

I guess there is a way of achieving what you want, but i couldn't do it.
You can squeeze out a partition from your MyDocs partition. And use it to store the desktop linux.
Use this guide for repartitioning or gparted (You will have to export the entire device first to n9 either using ubiboot or by loading the rescue initrd).

After partitioning and installing linux using EFI. You have to export this partition to pc whenever USB is connected, a way of doing this is given in the repartitioning thread, but i couldn't get it done .
Then once that is exported, i guess you can specify what EFI file to boot from on the pc and it should boot without having to turn off the phone.