Yes, Speiser's theorem is an if and only if.

See Theorem 1 and "Corollary to Theorem 1" in Levinson and Montgomery's [Zeros of the derivatives of the Riemann Zeta-function][1]. Acta Math. 133 (1974), 49–65. 


  [1]: http://www.springerlink.com/content/dk48528205t15585/fulltext.pdf