No. This is explicitly stated in the paragraph above Theorem 1 of:

[Turner, Edward C, Test words for automorphisms of free groups.
Bull. London Math. Soc. 28 (1996), no. 3, 255--263.][1]

The author refers to Proposition 1.


  [1]: http://blms.oxfordjournals.org/cgi/reprint/28/3/255.pdf