Technically yes you can do that by attaching the plate to the lens tripod mount and the other end to the camera. But I've not tried it myself since it seems extremely troublesome when I have to change lens.
Just to clarify some parts... In the above picture I've posted, this is the Camdapter SlingStrap Pro (the one with handstrap). The non-pro SlingStrap version does not have the handstrap.
If using without the handstrap, you will have to attach it like below.
And I guess that if you are attaching it to the lens, this is how you will be attaching to it. The wear and tear from above comes from the time when I have to use satay sticks to push the strap thru the tiny space between the bar and the plate. This too, I've not seen too much wear since then.