Grand Canyon hiking is more difficult than mountain hiking because of the short days. In June you will only have a few hours in the morning and late afternoon to hike. I plan about half the mileage compared to the Colorado mountains.
On both rims you have no problem finding a place to hang. Below the rim the corridor and threshold areas are designated sites and they are NOT hammock friendly. In the primitive and wilderness zones the places to hang are very sparse.
Hammocks lose their weight advantage when you have to carry a couple of 20' 1" webbing and several cams. At the esplanade level you will find isolated sites where you may have one tree and a boulder with an anchor possibility. A couple of cams in a Tapeats canyon would be another possibility.
I love my hammock, but I go to the ground in the Canyon. If you have climbing experience and after you have double digit nights in the Canyon and in a hammock and still think it is a good idea then go for it.