No. Kropotkin and Marx never met as far as anyone seems to know. Kropotkin wrote about Marx and his theories a great deal, but I don't have the time right now so I'll leave this to get you started.

"Kropotkin did not carry his differences of opinion into the open, except in his relentless opposition to all forms of authoritarianism, which meant a constant state of warfare with authoritarian socialism as represented by the followers of Marx. Besides his opposition to him on principle he had a strong personal dislike for Marx,--who he never met,--largely due to Marx's treatment of Bakunin. Marx, according to common report, had helped spread false rumor that Bakunin had been in the employ of the Russian secret service.

Yet when these two once met at the home of George Sand, Marx greeted Bakunin effusively. Kropotkin could not tolerate what he regarded as unpardonable hypocrisy. This feeling was intensified by the discovery that parts of the Communist Manifesto had been lifted almost word for word from a work by Considerant. Kropotkin took almost a boyish delight in scoring anything on Marx, and, furthermore, he had contempt for him as a politician."

Peter Kropotkin, Kropotkin's Revolutionary Pamphlets. Roger N. Baldwin, editor. Vangaurd Press, Inc. 1927