Each box in Pokemon R/S can hold 30 Pokemon, and there are 14 Boxes. So thats... 30 x 14 = 420 Pokemon you can store, plus the 6 in your squad. Cos your Dex contains 202 max (not counting the National Dex), you won't even need half of that, since most of them are gained by levelling. Although if you're like me and have all the Colosseum Pokemon in your R/S carts, you may start to need the extra space, and if you do a lot of breeding, you'll need even more.
Although it would be funny to have Pokemon Box and L100 of each Pokemon, including unevolved forms as well. :-)