You should be able to.. but honestly.. I've never checked it. Once a conversation is closed, if necessary a new one should be started instead of continuing one that may (and most likely is) on another topic/issue. If it's simply a continuation of an old issue (like in moderation) it's one more strike.
As for opening from the aspect of the conversation starter.. I doubt it.
I had someone send me a snotty message and then lock it so I couldn't reply, thinking he was being clever. I wanted to unlock the message and reply, to show him he was not (yes, I know it's a bit childish but it sometime has to be done).
Anyway I found an addon which does exactly what I need, i.e. allows admins & mods to reply to locked conversations:
Small addon that will allow admins and/or moderators to reply to locked conversations. There are two options for the addon, one to allow admins and one to allow mods. Options: Example: Make a small donation if you love this addon