Size of pots needed for hydro grow

Hey everybody, to my understanding hydroponics keeps roots small because the plant doesn't have to expend energy to grow them because all the nutrients are supplied directly. That in mind, do you think 2 gallon pots (1 gallon pot stacked on top of another) is big enough to support adequate root growth in my hydro setup from seedling through flowering. Here's a link of my setup, any advice appreciated, thanks alot!

http://www.lmcwholesale.com/products...%206%20Cell%22

what is that!! flood and drain in buckets, or minei aqua farms!surely the pots are part of the kit???????????????????????????????????????

yeah the pots are part of the kit, they're the dimensions I listed above, is this a big enough volume to support adequate root growth through flowering?