for EUR max = 5.000.000 http://www.interactivebrokers.com/e...?exch=ibfxpro&showcategories=FX&ib_entity=llc
IB's listed maximums are for a single order...so yes you can enter large positions. If you are trading such size then you can easily afford a good front-end like Buttontrader...which allows you to enter how ever big of size you want and it will automatically break the order down into smaller orders that execute instantly. ie enter a 20 million buy for AUD, will split the order into 8 mill, 8 mill, and 4 million and execute them all (assuming the offer is there to fill this)
You can also set up a Scale Order in TWS with a minimum price difference (i.e. 0.5 pip). For example, to buy 20M AUD at .6500 you could buy 4M each at .6501, .65005, .6500, 64995 and .6499.