I would argue that Chris McCandless probably thought that he had found his spiritual reality when he arrived in Alaska, but then eventually realized that he did not. Here are several examples to support this opinion.
1. After years of planning for and traveling toward his ultimate goal of entering the wilderness and living off the land, Chris finally arrived in Alaska and struck out on his own. During his first several weeks in the area around the bus, Chris seems to have been doing quite well, well enough to believe that he had reached his goal (he made plans to return to "civilization" when the weather made it possible).
2. If Chris had survived, however, I think that he would have had to admit that by using the bus as his habitat, he was cheating a little because he used a completely artificial intrusion to shelter himself--a "house" that rusted, decayed, and was an eyesore to Alaska's wilderness.
3. The most striking evidence to demonstrate that Chris most likely did not feel completely spiritually fulfilled appears in his note that he left asking for help and the fact that he signed his real name to what we believe is his last written note (instead of signing Alexander Supertramp). His signature suggests that he had entered back into the world of reality.