Yes and yes.
I have tried quite a few different scenarios. No luck as yet. When I invoke a method on beanY (which does not have any @Begin annotations) I am thrown to the page resulting from @Conversational(ifNotBegunOutcome="fail") (as defined for that bean). It appears as if the conversation did not span the two beans.
Remove the @Conversational annotation. @Conversational enforces that the current conversation must have been started by the bean.
Aaahh... The small things in life ;-)
Did so and works like a charm !