Most of the key areas in Madera Canyon are public, and you don't need to be a guest to stay there. The only things that might be off limits is that, at least in former times, each cabin had it's own set of feeders in the back, which are good for bats and at that time Ringtail. So I suppose if you are interested in those types of critter, or in the rare event there is a rare hummer only using the back feeders, you might be out of luck.
Mid-late June is kind of a dead period, since it's too late for spring migration and the July-August Monsoons haven't started. If you can, you might consider waiting until then. That said, Pine Flycatcher, Berylline Hummingbird, and Rose-throated Becard are all still being reported, so there are certainly still rare birds around to make for a productive trip.