ANSWER:

This is permissible, providing the intention of fasting the fard fast was made prior to the athan of fajr or a night before. Not having suhoor has no impact on the validity of fasts but one would lose a great deal of reward for skipping this great sunnah. 

My question to you is that can one keep nafil fast (voluntary) and kadha fast (compulsory) together? If yes, then is it acceptable if one keeps it(both nafil and kadha fast together) without doing suhur?