FMOD Studio does not have a built in synth, but you are able to build your own by using a custom plugin instrument. Take a look at the plugin API example bundled with the FMOD Studio API installation.
There is also a basic tone generator (FMOD_DSP_TYPE_OSCILLATOR) in FMOD Core that you might want to look into.
https://www.fmod.com/resources/documentation-api?version=2.0&page=plugin-api.html