What's your client doing with all these databases ? Seems a bit odd to be having all these databases.
The joy of unlimited databases
Is he overloading your server ? If not, then you have no worries, however he tries to access a large number of these database concurrently, then you'll probably start to notice performance issues.
The key thing with databases is that the schema is designed well and queries are optimised. I guess you have no input to the design ? MySQL will handle large numbers of databases OK as long as you have sufficient resource on your box.
Personally, I'd hate to be running an app that creates so many individual databases. I've seen similiar problems where a system generates a database per customer rather than linking a customer ID field to common data.
You'll have to monitor and see how things develop.