Yep, they can, probably not commercially, but for home use they tend to produce superior results. One of my favourites for growing in tubs was spuds. A well drained 45 gallon water butt raised off the ground, a layer of peat based compost, half a dozen seed potatoes, layer of compost. as the stems grow, keep topping up with compost until you reach the top, gives you spuds all the way down. With carrots and beet you will need quite large pots, about 15 inches diameter, sow quite thickly and use the thinnings as they grow. Carrots can be sown with spring onion seed or onion sets, helps to keep carrot root fly at bay.