ANSWER:

These 2 rakahs are to be prayed before the fard prayer of fajr and not before the adhan of fajr. 

Hence tahajjud which is to be prayed before the Adhan of fajr and these 2 rakahs of sunnah of fajr cannot be combined.

Sheikh, is the 2 Sunnah rahkats before fajr that the prophet (saws) said it is better than the world and everything in it is that considered as tahajjud or does it only have the first reward. if I make the intention to follow that Sunnah and also make the intention to pray tahajjud do I get both the reward. The reward of tahajjud and the reward of the 2rakats before fajr.