My understanding is that the majority of the aroma compounds in hops are not, in fact, alpha acids, but are instead oils. The oils and related aroma compounds will volatilize off during the boil and, thus, hops that are added early will leave bitterness without much aroma.
My understanding is also that the amount of oil in a hop is (often) directly proportional to the alpha acid level. Thus, a hop with a big alpha acid load like citra or magnum will also produce a big aroma.
The distinction between "aroma" hops and "bittering" hops is based on traditional brewing techniques, largely developed around German lager styles. Czech Saaz, for instance, is sometimes thought of as an "aroma" hop because it imparts a pleasing aroma to pilsener beers. Magnum, on the other hand, is often reported to have little flavor and a vegetal aroma; nevertheless, its high alpha acid load makes it perfect for bittering.
Today, many breweries use high alpha acid "bittering" hops like Citra and Simcoe as aroma hops or in dryhopping. Pliny the Elder, for instance, relies heavily on Simcoe. Many American IPAs use Cascade as both a bittering and an aroma hop. In short, the classification of hop varietals for "aroma" or "bittering" is, to some degree, no longer done.
That said, there are good reasons not to use hops randomly or interchangeably. The first is that different hop varietals have distinct flavors that may be not to your taste, or style inappropriate. The taste and aroma of cascade hops, for instance, would probably not go well with the funky flavor of a Belgian Golden Strong, or the delicate taste of a pilsener. On the other hand, using a low alpha-acid hop like Tettnang or Saaz to make a bitter beer like an IPA would call for such a high volume of hop matter that undesirable secondary flavors like grassiness or vegetalness would start to come through.
