No you can't. Possession of all the parts to convert a firearm into a full-auto firearm are themselves classified as a fully automatic firearm. They require the same paperwork and tax procedure that purchasing a fully automatic firearm does, and that procedure (for non-government agencies) was essentially abolished by an amendment to the McClure-Volkmer act in 1986.
You are confusing spare parts kits with conversion kits, or you are talking about illegal products (such as drop-in autosears, possession of which without the tax and paperwork is a felony).