The short answer is, No. Neither the Moodle has this capability built-in nor there exist any Open Source add-on to do this. You can find more discussions in this forum through the Advanced search https://moodle.org/mod/forum/search.php?id=5
For a longer answer, one should distinguish between two approaches.
a) At Moodle site level
This is what you were thinking of. And you also guessed the problem. Once the databases grow independently, they can not be put together, there'll be so many collisions. Considering the scope of Moodle, with a dozen of entirely different built-in tools (called Activities
) and hundreds of tables in the database, this is a complicated task. I remember in the old discussions, a Moodle Partner
(who also fund the Moodle project) had shown interest. If you can raise funds, that would be neat, and a big enhancement.
Another idea. There is Moodle fork iomad (iomad.org) which has added multi-tenancy to Moodle. If you can convince iomad that a satelite Moodle is a tenent, it imight be able to reimport the satellite Moodles to seperate tenants.
b) Specific to an on-line exam (Quiz)
If you szenario is just a one time distributed exam, it must be easier to copy just the resource Quiz to satellite Moodles and then re-import them with the student submissions. You might want to ask in the Quiz forum https://moodle.org/mod/forum/view.php?id=737
Whatever approach you take, the user registration will affect the solution.
There is good news on the satellite side though - read "Moodle for android offline users" https://moodle.org/mod/forum/discuss.php?d=373051