Probably, yes. You can just right-click and select compress as tar. If it finishes without any errors then it should be good to go.
You will only be able to shrink /home as much as gparted will let you, which is generally no less than the amount of drive space actually being used. For instance, if you /home is 9gb and you're using 5gb then gparted should not let you shrink that partition any more than 4gb max.
Regarding backing up /home:
I actually followed Granny's advice from a different thread but just backedup my user directory rather than all of /home:
If you don't have a Linux-formatted external drive, you can tar your /home directory before copying it to any external media. You want to use
modifiers to preserve ownership and permissions. (Some say this isn't strictly necessary but I know it works, so I use it.) When you restore you want to use
to make sure the files are restored with your ownership and permissions intact.
I ran:tar -cvpsPf /home/<username>.tar /home/<username> --exclude=My_Network
This created a tar file in /home named newt.tar containing everything within /home/newt, however I had to also exclude a network mounted directory which is probably not the case for you. After than, I gzipped it to make the transfer over wireless a bit quicker using this command:gzip -c /home/<username>.tar > /home/<username>.tar.gz