An interesting question. I would say no. A paradox is a conceptual contradiction—cowards can't literally die many times before their death. It isn't possible. However, the line feels true, because of how they suffer. A pun, by contrast, swaps words that sound the same but sound different (like "grave" [serious] and "grave" [a hole where you bury a body]) in the literary terms page's definition of pun. Puns involve substitutions of language and depend on fooling the ear for their humor.
So, the two concepts are related, but unless you hear a specific word swap in that line, it is a paradox but not a pun.