No, you can't enter this area without a Special Use Permit from Corvallis Parks & Recreation.
Yes, this is a public site and you can reach the cache from outside the gate.
"Noyes Natural Area" mainly features wetlands, which is an ideal habitat for many forms of wildlife. The area is a work in progress. While there is now a 1/4 mile loop trail through the wetland habitat, a parking area has not yet been designated.-- From the Corvallis Parks and Recreation website