Does Pip get rich?
The answer to this question is "Yes, but..." with the "but" being an essential element of the novel.
In chapter 18 of Great Expectations, Mr. Jaggers tells Pip that he
will come into a handsome property. Further, that it is the desire of the present possessor of that property, that he be immediately removed from his present sphere of life and from this place, and be brought up as a gentleman - in a word, as a young fellow of great expectations.
Pip immediately assumes that this mysterious benefactor is Miss Havisham and eagerly jumps at the chance to improve his living conditions. However, just before the end of part 2 of the novel, Abel Magwitch, the convict whom Pip showed kindness to back when he was a young boy, reveals that he is in fact Pip's benefactor. Shocked and appalled, Pip decides that he can no longer use the money of his fortune, now that he knows its true source.
When Pip tires to help Magwitch leave London without being apprehended by the police, his plan is foiled and Magwitch is captured. The government will take all of Magwitch's property--including the fortune Magwitch left to Pip--so Pip's fortune is gone (though Pip isn't upset about this, as he wasn't intending to use the money any longer).
Pip falls into extreme debt given the lifestyle he was accustomed to and the money he no longer has. Joe saves the day, paying off Pip's bills.
By the novel's end, Pip promises that he has learned the value of hard work and is happy with the decent living he makes running the Eastern Branch of Clarriker and Co. He eventually becomes a partner and "lived frugally, and paid my debts, and maintained a constant correspondence with Biddy and Joe." As Pip says, "We were not in a grand way of business, but we had a good name, and worked for our profits, and did very well." Thus, he seems satisfied, though he is no longer a gentleman of great expectations.
So, the ultimate answer to your question is, "Yes, Pip gets rich, but then he becomes very poor, and finally he becomes a man of stable means."
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