Doesn't appear to be so. A quick look at some sites produced more likely origins of the words f*ck and sh*t. Long but interesting reads, and the acronym above is also addressed.

http://www.snopes2.com/language/acronyms/****.htm

http://www.snopes2.com/language/acronyms/shit.htm

EDIT: Since the board doesn't allow the full spelling of the "f" word, be sure to replace the asterisks in the above link with the correctly spelled words to get to the page.