You can run a community of sorts, but the feature list will be sparse. The only viable system sans-database that comes to mind is plain-text.
I'm a member of a forum that had an old system in the beginning that used plain text "database" for a very long time. Performance was fairly reasonable at 5000 visitors per day, if the daily hit counter was to be trusted. They since moved it to SQLite, which is very reliable in its own right, and now it's Postgres. It was only now that we got searching as a "feature".
The system was written originally in PHP 4.x, but they did move it to 5.x. I'm not sure what version they use now. I do know they were running ancient hardware and was up solely due to the charity of the admin.
I think there was an index file that stores new topic summaries, as there was no field for titles, when they were created.
They used microtime() as the ID, but the topics were stored by splitting it to 3 digit directories.
Seconds as 1234567890 and decimal 0.12345618 were combined to create /123/456/789/012/345618.html
There's no registration system or other way to identify the user so I believe the posts were separated by some kind of entry separator in a single file.
I think the pagination system created an array of sequential IDs and checked to see if files existed in those directories. There were no numbered links for pagination, only next/previous and if you reached the end, the next page would be blank.
There's no reason you should ever get laughed at for being curious.