yes!
I use LinuxMint 6 (it's distro from Ubuntu 8.10) and TinyCore Linux 1.2.
you must copy 2 files (tinycore.gz and bzImage) from cdrom with tinycore1.2.iso or later and modify your existing bootloader to boot off them.
for copy use in terminal sudo cp . i copied tinycore.gz and bzImage just in /boot/
I like mint - u can just click mouse on menu "open as root" and u don't need to type commands in terminal. ;-) -fast and easy! ;-)
in Ubuntu:
press alt+f2 for "run" window . type gnome-terminal
in terminal type:
sudo gedit /boot/grub/menu.lst
(for editing of booting menu)
then in gedit go to line like
title Ubuntu 8.10, kernel 2.6.27-7-generic
root
kernel
initrd
quiet
after that lines type:
title TinyCoreLinux 1.2, kernel 2.6.26
root (hd0,5)
kernel /boot/bzImage quiet
initrd /boot/tinycore.gz
Save file menu.lst. Reboot.
for example, its a part of my menu.lst:
title Linux Mint Universal Edition, kernel 2.6.27-7-generic
root (hd0,5)
kernel /boot/vmlinuz-2.6.27-7-generic root=/dev/sda6 ro quiet splash locale=uk_UA
initrd /boot/initrd.img-2.6.27-7-generic
quiet
title
?? TinyCoreLinux 1.2, kernel 2.6.26
root (hd0,5)
kernel /boot/bzImage quiet
initrd /boot/tinycore.gz
(i use mint, it's much easy for newbei, like me ;-), i don't use ubuntu about 2 years - ubuntu don't work on my note Acer Aspire... i use ukrainian locale. mint and tcl boots from sda6. i have 8 partions - ntfs, hfs+, ext2, ext3, reiserfs... )
Good luck, hackers! ;-)