Aacording to Weld the docs:
The conversation context is active during any JSF request.
and at the code of org.jboss.weld.servlet.ConversationPropagationFilter
One can read
FIXME This filter is specifically for JSF and should be repackaged or split up to support non-JSF environments.
All that indicates that conversations are only for JSF. Please make them available for plain servlets (and JSPs)