That is true, but I was thinking more along the lines of a tyrannical government than an EMP. You are probably correct, and I was thinking of HAM operators personally logging into the BBS to upload the files and data they received. Having it done automatically by the BBS computer is definitely an idea though.
That wouldn't be that hard to do. I wrote a piece of code like this that ran as a service on windows servers and contacted the main database clear across the country many times a day. Only data since the last time stamp was exchanged. Need to add a few bells and whistles like logging, recovery, and notifications.
What you are describing is a form of a “store and forward” network, which has fallen out of favor due to the incredible bandwidth we have today.