If the /home on the root partition contains files and data you want to keep, then yes. If not, then you can simply wipe it away. I recommend doing this from an Ubuntu installation disk (or administration mode if you know how to use that - you don't want to be logged into the GUI for this one on your live box).
If you are using the live CD environment, you will need to mount your root partition - open a terminal and type
mkdir -p /mnt/filesystem
mount /dev/sda1 /mnt/filesystem
Modify /dev/sda1 to reflect your actual root filesystem. Then in the terminal you will need to
cd /mnt/filesystem as the following instructions about editing the /etc/fstab file apply to the one stored on your actual Ubuntu installation's root partition, not the one in the liveCD environment.
You'll need to edit the /etc/fstab file to tell it to mount your home directory disk partition to /home. On my machine, my home directory is on /dev/sda6, which uses the ext4 filesystem. So the line in my /etc/fstab file looks like this:
/dev/sda6 /home ext4 defaults 1 2
This tells the kernel to mount that partition in /home as ext4 (replace if you use a different filesystem), with default options (usually OK), and the 1 and 2 indicate it is to be backed up by dump (if you use that - safe to ignore otherwise) and will be checked if the system detects filesystem corruption (you probably want this).