Yes, you must tell HR. Going in, realizing you are setting the stage for your dismissal-your way. HR is not there to help you-however, legally they cannot destroy your file etc. and the documentation will be there to set the stage for your departure, your way. And, yes, put your manger on notice that s/he is accountable to answer 'for the record'…of course. 
Many of us who have left were one fruit loop short of a bread basket….over time you will heal and you will be stronger and empowered. It will work out for your good. Happy Thanksgiving. Be thankful for all you have, including this scenario. In the long run-YOU WIN.
