It would, but you would also need to do some more things. The default permissions of
/tmp are this:
# stat /tmp
Access: (1777/drwxrwxrwt) Uid: ( 0/ root) Gid: ( 0/ root)
Since the permissions of the link are the permissions of the target, you will have to change the permissions of
~/tmp. At the least, it should be world-readable and -writable:
chmod a+rwx ~/tmp
t bit should also be set (see What is the "t" letter in the output of "ls -ld /tmp"?):
chmod +t ~/tmp
There might be other problems. If any directory in the path for
~/tmp doesn't have execute bit set for others, this folder will be inaccessible for most users.
I missed the obvious flaw in this:
Any attempt to use
/tmp before your home directory is available will fail.
This might be one place where bind mounts are better than links.