Hiya,
To address your question - yes, you may use the 20 x 10 temporarily, but your dragon will quickly outgrow it. I would guess in only a few months, as well. I would say that the absolute biggest dragon I would keep in that size would be 10 inches, and I would really rather swap much earlier than that - maybe 8 inches or so, preferably even earlier.
Floor size - that is length and width - are more important than vertical space or height. That said, beardies do love to climb and could be considered semi-arboreal. I would not go any shorter than 1.5 foot tall and would recommend using that vertical space.
The size enclosure an adult dragon needs depends on the individual. A small dragon, like my Guacemole (17.3 inches as an adult) /can/ happily live in a 40 gallon breeder (about 3 foot by 1.5 foot by 1.5 foot). That said, I still have him in a 4 foot by 2 foot by 1.5 foot.
MOST dragons will be happy in a 4 foot by 2 foot by 1.5 foot enclosure. Giant ones, aka 21 inches or bigger, not so much. As a bare minimum guideline, I like to use the 1 x 1.25 x 2.5 rule. Your tank should be as tall as your dragon is long, as deep as 1.25 times as long as your dragon, and 2.5 times as wide. Central bearded dragons are usually 14-24 inches long, with the majority being spitting distance from 18 inches long. Therefor the usual recommended size of 4 foot by 2 foot by 2 foot (48 w x 24 d x 24 h) is just a smidgen bigger than the absolute minimum size for the average BD (assumed to be 18 inches), which would be 45 w x 22.5 d x 18 h.
In short, the smallest I would ever even consider is 40 gallon breeder, but I still think that's too small. 4 foot by 1.5 foot by 1.5 foot is decent, 4 foot by 2 foot by 2 foot is usually perfect. For an animal as active as a beardie, though, a valid argument can be made for "as big as you can affordable and accurate heat and maintain".
Hope that helps,
-Ellen