short answer yes, anything is possible
long answer, its going to be a tough project
to avoid the DAC simply have your computer talk straight to your microcontroller via RS232 or USB whatever. to digitally tune a radio you must have access to component level. i'll assume you do.
in many ways it matters what type of radio (is it a digital radio receiver, is it AM/FM with superheterodyne topology etc.) and how much access you have to its internals. even better if you are building the radio yourself, cause then you can achieve frequency synthesis or put a digital PLL on board. the PLL is what locks on to the radio station. the PLL usually adjusts the frequency of the "Local Oscillator" which mixes with the radio signal to get to a frequency you can hear. thus you must have microcontroller control the PLL.
Mr.Cool