[luau] Security Question

[W. Wayne Liauh]

Suppose I am logging in and doing my work as user1.

Then, while I am doing my work as user1, instead of running
Mozilla as user 1, I switch user to user2, then do my web browsing
and e-mailing as user2.

There is a default firewall, and neither user has the permission to read,
write, or execute any file that belongs to the other user.

My question:  will this little extra step improve my security over the 
regular way
of doing web browsing under the same user?