AFAIK, for all of the SAM3 microcontrollers, const Adc *p_adc points to 'ADC' which is the address of the ADC Control Register (ADC_CR) (0x400C0000U).
As you mentioned in your post, the routine returns a clock value. For the Arduino Due case this value in Hz is 21000000. Four times smaller of the main clock, normally, 84MHz.
The calculation of the ACD clock frequency is very simple:
ul_adcfreq = ul_mck / ((ul_prescal + 1) * 2);
where ul_mck is the main frequency of the board = 84000000
ul_prescal is a 32-bit clock prescaler set to 1 (0xffu << 8)
Here a raw example sketch for Due:
int ACTUAL_ADC_CLK;
void setup() {
Serial.begin(9600);
}
void loop() {
// get and print current ADC clock (in Hz):
ACTUAL_ADC_CLK = adc_get_actual_adc_clock(ADC, SystemCoreClock);
Serial.println(ACTUAL_ADC_CLK);
while (1) {}
}