This request goes through EP0, so yes, you could use the EP_0_ISR_ExitCallback(). But this function executes on any EP0 interrupt.
There is a more specific function that is executed when there is a class request (your case). Refer to the function USB_DispatchClassRqst in USB_cls.c.
In the end of the function, you can write code between this lines:
/* `#START USER_DEFINED_CLASS_CODE` Place your Class request here */
/* `#END` */
Or you can implement the USB_DispatchClassRqst_Callback() function and define the USBUART_DISPATCH_CLASS_RQST_CALLBACK.
