Not really - Isaiah 53 is referred to by John and Paul (Romans 10:16). It clearly refers to the Jews, namely the unbelieving ones:
John 12:35 Then Jesus said unto them, Yet a little while is the light with you. Walk while ye have the light, lest darkness come upon you: for he that walketh in darkness knoweth not whither he goeth. 36 While ye have light, believe in the light, that ye may be the children of light. These things spake Jesus, and departed, and did hide himself from them. 37 But though he had done so many miracles before them, yet they believed not on him: 38 That the saying of Esaias the prophet might be fulfilled, which he spake, Lord, who hath believed our report? and to whom hath the arm of the Lord been revealed?