You cannot trade your pokemon from R/B/Y/G/S/C to your R/S/E/FR/LG games it is unfortunately impossible. the reason is that some of the mechanics are different such as the transfering system when doing a trade. In the old days each pokemon was sent to each player one at a time but now both pokemon are sent at the same time. The other reason is that the IV range is different. In the old days it was 1-15 now the range is 1-31.
If you mean can you use Pokemon Box to trade pokemon from the old games then no you can't. If you mean to ask if you can trade between Box and FR/LG/R/S/E then yes you can but you have to reach a certain amount of pokemon in your pokedex first I think but in FR/LG you need to have fixed the transfer machine on 1 Island first with the ruby and sapphire plates.