It is possible to program the PIC in the RN2483 with your own application code - but the PIC is not supported in the Arduino environment nor in the Atmel Studio environment. Instead you could download MPLAB-X IDE from Microchip and the associated compiler from Microchip (all free for commercial use) or use compilers from companies like CCS (www.ccsinfo.com)
However I would not do it that way. I use the RN2903A which is the same device as the RN2483 but supporting frequencies in the US and most other places in the world outside of Europe. They are pin compatible and have identical APIs so developing for one automatically means you are have a hardware compatible solution for the other just by changing modules. Both of these devices function conceptually like the old Haynes style modems. You send them commands and data over a serial interface and receive command responses and data over the same interface. Naturally it is not quite that simple, different frequency bands to setup, different limitations on payload sizes, time-on-air etc.
In my case I use an Arduino environment to develop applications on microcontrollers to communicate with these modules. Specifically I have use the STM32 and SAMD 32bit microcontrollers however the choice of these controllers was determined by other tasks they had to perform. Talking to the radio modules themselves is very simple. Having said that, keep in mind that I do not use any special function Arduino library functions (like software serial ports, software I2C ports, temperature / humidity drivers, PM sensor interfaces etc) instead I either write my own or I modify the libraries to achieve the performance and error handling capabilities that I need. If you want to stay with the Arduino environment, and needed a powerful 32 bit processor, then, based on my experience, the Atmel SAMD is a good option.