No, it is not legitimate. Purchasing gil offered by 'Real Money Traders' (RMT or 'gilsellers') is actually against the Terms of Service you agreed to when you created your account, and thus, if SE discovers you have purchased said gil for real money, your account will not only be suspended, but completely deleted. RMT harms the legitimate economy in the game and ultimately ends up costing you as a player. So ignore the temptation to deal with the devil so to speak.

Besides, it's not that difficult to get gil nowadays legitimately via the Challenge Log, the Hunt and levequests, so why people are still buying illegal gil for cash is beyond me.