Seeking solitude is not the same as finding loneliness at all. Being secluded from others by choice is an purposeful act a person makes. This does not mean you are lonely, but rather want to be alone and in that solitude you find peace, calmness, relaxation, etc...
Loneliness can happen in a marriage, in a crowded room or when alone. Loneliness is not something anyone seeks. It's a word that typically has a negative connotation indicating a person that wants connection with others, but is unable, for whatever reason, to find that connection.
I would not seek poverty, sickness or other such things in an attempt to get closer to God. If i found myself in these things, or in loneliness, then i may then reach out to God. But i see nothing in scripture that says to seek out to put ourselves in negative situations to get closer to God. And Christ did not seek to be lonely, but rather he sought solitude from others. He Wanted to be alone, not in some psuedo-spiritual attempt to get closer to God by making things bad for himself, but rather getting alone with God by choice when things were already bad.