Установка загрузочного Debian Jessie на внешний HDD с разделами

Да, можете.

и вот что произойдет:

[root@server ~]# mkdir new&&cd new
[root@server new]# echo -e "#! /bin/bash\nrm -rf" >remove.sh
[root@server new]# cat remove.sh
#!/bin/bash
rm -rf ~/new
[root@server new]# ls
remove.sh
[root@server new]# bash remove.sh
[root@server new]# ls

(empty here,all file and directory are deleted, but we are still inside this "new" folder before we change our directory)
[root@server new]# cd ..
[root@server ~]# ls new 
ls: cannot access new: No such file or directory