Do RSA keys contain a checksum mechanism?
No, there is no checksum built-in to the RSA keys per se. There is no need for that.


  Does this breaks the key ? Or changes the key internally, without
  breaking it ?


[EDIT] It was rightfully pointed out to me that at least one of the statements I typed (in haste) was plain wrong. Now that the answer has served its initial purpose, I've removed my badly worded and therefore wrong statements and just duplicating here the link to a much better explanation of things (which I really liked):
Why does my SSH private key still work after changing some bytes in the file?