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.

This is an interesting question and one left open to the interpretation of each individual reader. I believe a compelling case could be made for either position. However, I'm inclined to agree mstultz72.

McCandless was reckless and foolhearty in his great Alaskan adventure. As noble and inspiring as the idea of his quest might be, his preparation and lack of knowledge create a situation ripe for disaster. Spiritual reality is a lofty goal, but what is it worth if you have no one to share it with? It reminds me of the old conundrum: If a tree falls in the forest but no one is around to hear it, does it make a sound?

I'm not sure I'm helping you much with your essential question and in supporting your argument. Unfortunately, the only clues we have to what Chris did achieve are the rambling scribbles he left in the margins of his books. It seems to me those might be your best sources for quotations.

I know this won't help you much, but I don't think Chris McCandless entered the spiritual realm.  I think he only existed in the ethical one.

Spiritually, McCandless was too full of hubris.  He thought he was much more accomplished as a naturalist than he really was.  Not to mention, he was in denial of too many of his problems, especially his own identity.  He invented an alter-ego (Alexander Supertramp) to escape the realities of his own shortcomings communicating with his family.  In short, he insulated himself by escaping into the wild.  He lived alone to spite others, not to be at peace.

Chris may be extolled for his ethical virtues: self-sufficiency and asceticism.  But, he attained them at the exclusion of others.  Man cannot be spiritual in a vacuum; a spiritual man must be in the world, though not of it.