Greg, "direct" connection to FileMaker is through XML web publishing (with or without PHP) or ODBC/JDBC sharing. These require FMServer. FMSAdvanced, if you want to use the xDBC's.
I've never heard of anyone making a request to directly communicate with objective C. But that doesn't mean someone has tried!
There may be plug-ins that would also allow the communication you need.
At one point I started to port my .NET connector to Objective-C but don't have time to finish it any time soon. There are a few XML libraries out there for OC in addition to the native classes. So you can certainly do it through the FMS XML engine.