The answer is yes, provided that $M$ has a faithful normal semifinite weight (this always exists) that is also semifinite when restricted to the centre (this I'm not so sure how easily can happen). 

When $M$ has a faithful normal semifinite weight $\varphi$, with $\varphi|_{Z(M)}$ semifinite, consider the modular group $\sigma_t^\varphi$ associated with $\varphi$. For each $t\in\mathbb{R}$, $\sigma_t^\varphi$ is an automorphism of $M$, and in particular it preserves its centre. This means that 
$$
\sigma_t^\varphi(Z(M))=Z(M), \ \ t\in\mathbb{R}
$$

These conditions, by Takesaki's Theorem (IX.4.2 in Takesaki 2, or [JFA1972][1]) are equivalent to the existence of a conditional expectation $E:M\to Z(M)$, with $\varphi\circ E=\varphi$. This last condition forces $E$ to be faithful and normal. 


  [1]: http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&review_format=html&s4=takesaki&s5=expectation&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=1&mx-pid=303307