NRF24l01 with Atmega 32u4 and internal clock
You ask a yes/no question, to which the answer is yes, nRF24L01 as a serial peripheral device will work as well as if you had used an Arduino UNO or any other microcontroller, provided the SPI bus is correctly initialized.

Generally you want the following in the setup() part of your sketch/program:

  pinMode(CE_pin, OUTPUT);//chip enable set as output
  pinMode(CSN_pin, OUTPUT);//chip select pin as output
  pinMode(MOSI_pin, OUTPUT);//SPI data out
  pinMode(MISO_pin, INPUT); //SPI data in
  pinMode(SCK_pin, OUTPUT);//SPI clock out

  digitalWrite(CSN_pin, HIGH);//SPI idle
  digitalWrite(CE_pin, LOW);

  SPI.setBitOrder(MSBFIRST);//SPI Most Significant Bit First
  SPI.setDataMode(SPI_MODE0);// Mode 0 Rising edge of data, keep clock low
  SPI.setClockDivider(SPI_CLOCK_DIV2);//Run the data in at 16MHz/2 - 8MHz
  SPI.begin();//start up SPI library