Feeling alone and being alone are two different things, and in I Am the Cheese, we observe both. Adam feels alone because of deceit – being lied to and having to lie creates a sense of distance between him and everyone around him. Honesty is such a vital part of human connection that, without it, isolation takes over. Unfortunately for Adam, he is also alone in a more physical sense: on his solo bike ride (in his mind), and also in the hospital, where he is an orphan with no friends or family.
Adam is not isolated; he is surrounded by people who constantly interact with him and, for the most part, help him out.
Adam enjoys being alone. If he didn't, he wouldn't have taken the solo bike ride.