No. If your /home partition is on sda4 and you select to install a new OS to sda3 and format sda3, sda3 data will be gone, sda4 data should still be there. I haven't installed with a separate partition for /home for multiple operating systems. I can see possible problems with that but they may be resolved fairly easily by someone who is experienced at it. The type of data you are referring to (Pictures, Movies, Documents) can easily be put on a separate partition and should be accessible from any without conflicts.
Formatting my root partition (/dev/sda3) to install a new OS will automatically delete every file I have in my /home partition (/dev/sda4), even if I expressly say to not format it, just because is used by Ubuntu as /home directory and mounted under /home/username?