The power to corrupt the database is definitely there, since the functions run as the system user of the database server with full access to the filesystem. So, if you blindly start writing into the data files and deleting important logs, it is possible that your database will be corrupted.

Additional types of denial-of-service attacks are also possible, such as using up all memory or opening all IP ports. But, there are ways to overload the database using plain SQL as well, so that part is not much different from the trusted database access with the ability to just run arbitrary queries.

So yes, you can corrupt the database, but please don't do it on a production server. If you do, you will be sorry.