Mere mods cant. Only pukka site admins such as GCO and BCO can delve in to your PMs. I know they dont as a matter of routine and they would only do it if they had as really good reason. So fear not, buck-fuck mods cannot.
Absolutely fair question, although I was surprised that you thought that they might be able to. Anyway, they can't and roadster280 is spot on with his comments about database access. I did mention this in the article below, although I will now extend it to mention that mods can't read PMs:
The damage from disclosure of your posts in private forums and personal messages are down to what you post or send. Your private messages are gone when you delete them although may still exist in our backups. They are not stored encrypted in the database and could be read.
I should add to that that there are 3 people with access to the ARRSE DB - me, BCO (both too busy to care what is said in PMs) and a German server administrator who I assure you couldn't care less what you write and could probably only read them if written in binary anyway! Oh, and our data centre don't have access either. For the sake of completeness we do backup to a remote server (in Switzerland) every night and don't encrypt the ARRSE DB, although its transmission is secure.
So as I said, don't assume they are 100% private but don't worry either.