According to several sources, no. A deindexed site should not pass rank to another site (usually deindexed penalties mean that the site is spammy and will "hurt" sites it links to).
However, it can pass some rank and power indirectly. For instance some web crawling services use other search engines to index sites in their database. Maybe google hates you but you manage to get other se to love you and the fact that you rank so well in another search engine can pick up with Google.
I have optimized several sites for Bing and (google analytics installed of course) have seen that google actually starts giving you better rankings if they see you get "genuine" traffic from other search engines.
... They say that analytics data is only used to have transparency... Well, in my opinion no. Google analytics is the biggest spy on the web and big g uses this information constantly.