The easiest thing is to check SMTP, but also enable AWstats. I have not gone to the effort of actually installing AWstats to look at the data, but the text file that is produced by hmailserver is easily understandable.
Also, you may just want to keep the Administrator program open and load status > status and just check the number of processed messages.
However, out of the box, hmailserver is quite good at anti spam. Unless you allow, local domains and ones that you specifically set up a route for are the only ones it allows delivery for.
On top of that, it has pretty good internal anti spam for the mailboxes you host as well - (DNS, SURBL, grey listing and white listing).
So, basically, monitor over the next few days.
I have been using hmailserver for roughly the past 6 months and have not had a problem with spam regarding the out of the box settings - unless you specifically allow something