I was checking out the custom exhaust hanger and was wondering if this helps hold an aftermarket exhaust any better or what does it do besides cosmetics?

The one I produce is cosmetic as well as functional as it also allows you to eliminate the passenger foot peg brackets. It is powdercoated and lazercut.
Very strong. Click on the link in my signature. It is made for stock AND aftermarket pipes and attaches at the same location the stock one does.

If you do not add the exhaust hanger, will it eliminate the ugly strap on the can?

for aftermarket exhaust? most manufacturers use those straps.

The strap holds the can. the bracket or "hanger" holds the strap . The stock can has a flange. Most aftermarket use a strap.

As was already said...if your can has a strap, you cannot get rid of it unless you have a mounting tab welded to the can itself.