Was Allen Ginsberg wealthy?

No. There's even a comical poem he wrote about getting mugged. They got his money and a few of his possessions but they left $40,000 worth of poems on slips of paper that he was carrying in his pockets.

He didn't seem to care much about money. Many people knew Allen--I was one of them--and I never had a single conversation about material goods or consumerism with him. He just didn't care. Whatever restaurant was nearby, especially if it had the Chinese food he enjoyed most, was just fine. If he'd wanted to make a lot of money, he could have left Ferlinghetti's City Lights Press and gotten a fat deal from New York publishers--eventually Harper did pay him well--but he stuck with City Lights and his friends as long as City Lights would publish him. His digs in New York were quite ordinary. He liked travelling, but not to luxury resorts.

According to his biography, Allen Ginsberg lived modestly, wore second hand clothes and gave money to charities. Materialism was not as important to him as his writing. He was not poor and he traveled a great deal. Like most poets, he was never rich.