The "databases" in mysql are really catalogues, is has no effect on its limits whether you put all the tables in one or each in its own.
The main problem is the table cache. Without tuning it, you're going to have the default table cache (=64 typically), which means you will be closing a table every time you open one. This is incredibly bad.
Except in MyISAM, it's even worse, because closing a table throws its key blocks out of the key cache, which means subsequent index lookups or scans will be reading actual blocks from disc, which is horrible and slow and really needs to be avoided.
My advice is:
- If possible, immediately increase the table cache to > the total number of tables
- Monitor the global status variable Opened_Tables in your monitoring; if it increases rapidly, this is bad.
- Carry out performance and robustness testing on your the same hardware in a non-production environment (if you are not doing so already).