No I do not think that Eustace Conway is a transcendentalist. Although he appreciates and lives off of nature he doesn't believe that the trees and the rivers and the animals have souls and are capable of demonstrating discipline. Eustace also doesn't believe that nature earth holds a spirit or divinity to god that is overpowering to all life. Transcendentalists, like Emerson, hold nature and all living things as equal to human kind. I think that both men appreciate nature and recognize the importance of it, but Emerson has a different idea about nature's spirit. Eustace finds spirituality within himself through nature, but Emerson believes there to actually be spirits in nature.
Gilbert doesn't think Eustace is a transcendentalist either. She knows that he uses it and recognizes its beauty but Eustace doesn't do this because he has deliberately thought about it. He personally experiences life in nature and is able to form this bond with it through his personal experiences. Emerson on the other hand is being philosophical about it. He isn't emerged in nature as Eustace is he rather is being hypocritical and telling people how important and valuable nature is and how they should be connected to it because they are part of nature.