No, not really.
ColdFusion Builder is just an editing tool. It is probably way over kill if you are just going to do this once.
If you want to use CFML to write the server side code the will process a form and put it in a database -- something it is very good at and can do with one line of code for very simple situations for beginner codeer, (though most developers will quickly outgrow this and just role their own form processing.) -- you will need a server that runs a ColdFusion application server.
You could buy ColdFusion for your own server (Adobe loves to sell it to people) or you can contract with a hosting provider that suplies it for you, some of these are available for less then $10 (US) a month. But you may get what you pay for there. Or you can try one of the several alternate CFML applications servers that are now available such as Blue Dragon, Railio, etc.
But to actually write the CFML code there are lots of easy and free editors that are up to the job, including something as simple as notepad or vi.
Not to say that ColdFusion builder doesn't sound like a great tool (I've yet to been able to try it) if you are a ColdFusion Developer writing applicaitons day in and day out. But it is far from inexpensive.