It is most definitely possible with the DirectAdmin API, i would also be happy to help out with parts of developing such a script if you were to go ahead with the idea.
There are several companies offering order/billing/management scripts that will automate account creation in DA.
Here's a list of the ones I know of in my order of preference (mostly based on price) and with notes for each:
1. Whois.Cart (http://whoiscart.net) Cost: $35 one time per license
Very nice script. I was involved in the testing of DA integration. The most recent version is installed on one of my servers and will most likely go live with it in the next few days. Much more than you would expect for the low price. Well coded by the makers who are VERY dedicated to producing a high quality product at the lowest possible price. License purchase includes a special $6.75 domain reseller offer from DirectI!
2. ServNetix (http://servnetix.com) Cost: Ranging from $8.95/mo to $550 one time
Also a very nice script that I was involved in testing DA integration. Many more features than Whois.Cart and extremely powerful! Has the ability to manage every aspect of your hosting business. Well coded and again from makers who are dedicated to producing a high quality product. I have spoken with the owner of the company many times on the phone (located in the same city as we are) and he is very easy to deal with. Very dedicated and serious about his offerings! This is a complete automation and management solution! (personal note - if the cost was more feasible in our business expenses at this moment, I would take this product over ANY others!)
3. Modernbill (http://modernbill.com) Cost: Ranging from $24.95/mo to $499.95 one time
Recently added DA integration. I haven't used this product myself but it is highly rated by many hosts who do. Now offering DA integration and automation. Includes free $7.95 Enom account and other discounted offers. Worth looking into.
There may be others on the market but I am not aware of them. Maybe I'll keep this thread updated as I find out about more. Hope that helps!