well I changed the PersistenceContextType from EXTENDED to default (transaction) on the main SFSB, and this issue went away. The other SFSB (noteAction) was default already.
so not sure if it's related to the a4j:support tag anymore...
I'd still like to know if the a4j:support tag submits the form and if so, what happens in terms of method(s) called on the SFSB. I know that ajaxSingle will only submit that component of the form and not the entire form.