In terms of the words, somewhat. Going from one language to another will have an impact on the work. The impact may sometimes be small, but there is a chance that the original meeting and intent would be lost or altered by the changes. In terms of the actual story, I would have to say no. Many productions and films of Hamlet have changed the plot's setting from Denmark to elsewhere yet the overall plot has not been altered nor has the impact been reduced.
This comes from a fan of Shakespeare, and I admit my bias may be showing. There are purists, however, who would argue that changing anything in the work would cheapen it, but I disagree. If a work is strong enough, if the characters hold the audience's attention, then where the story takes place does not matter. Hamlet could take place on Mars and the story would still have the same effect as it has had for centuries.