But the problem is that we have a definition of "outside books" as the Rif defines it. The Rif says those are books that "explain the Oral or Written Torah with new foundations or principles that are not already contained in those books." And most of the ideas in the Ari don't seem to have a source in the Talmud. I think the answer to this is that in fact in the agadic parts of the Talmud, you do find things that hint to the basic principles of the Ari.
At any rate, never learn Kabalah with Ashkenazim. They always get it wrong and it has serious consequences when they do.
The best approach is this: If you have a daily session in Gemara in depth [about a hour] and one learning quickly [also an hour] then the Ari is a good idea to supplement to your daily routine.