I don't see why that wouldn't work as long as you have proper lighting for them, and with no fish you may need to fertilize them; I've done something similar myself.
However, you often save money (at least on shipping) if you buy more plants at once; would there be any way to set aside the money you would spend gradually acquiring them and instead buy them all at once? I just know that shipping adds up; usually $6 is minimum, so if you buy 1 order of plants that still fits in a small box instead of 3, you've saved yourself $12 right there.
Also, make sure you check out the for sale/trade section on this forum for good prices on healthy plants; it is by far the best source around.
Joy to the fishes!