What logging moodle does can be found in 'reports' which is queying mdl_logstore_standard_log table.
Go look at that. Think that's the only logs you got in the moodle interface that's related to forum postings/mail ... but no mailque. There are 9 tables for forums. If one did explain on all 9 of them, one at a time, one might see a column sorta related to what you are asking, I think.
"but I don't want to have a look at logs" ... Errr, uhhh ... sorry, but once moodle packages up whatever it's supposed to send, a cron job/task will attempt to send as many and as soon as it can - that's handed over to the mail server and it's que.
Other wise, 'bounces' (postmaster notifications which are in RFC guidelines for administering a mail server) don't come back to Moodle code they go back to the sending ***mail server*** ... and, I for one, would NOT want Moodle to attempt to handle that!
Do you have any tool to browse Moodle tables?
'spirit of sharing', Ken