If you know beforehand what kind of data you will feed in ("these are monthly sales of CPGs, with prices and promotion markers, and I want a point forecast"), so you can tune your setup ahead of time, that will likely be possible and already done, see various "expert systems" for certain specific tasks.
If you are looking for something that can take any kind of data and do "something useful" with it ("ah, here I am supposed to recognize handwriting and output ZIP codes, and there I should do fraud detection, and this input file obviously is a credit scoring task"), no, I don't think that will happen in a long time.
Sorry for an opinion-based answer to what might well be closed as an opinion-based question.
EDIT to address the edited question:
we have one column with categorical data, let's call it $y$ and we want to predict it from numerical data $X$ that is either dummies or real numerical data
This sounds like something that Random Forests are actually pretty good at. Then again, a "general-purpose" algorithm like RFs will likely never beat an algorithm that was tuned to a particular type of $y$ known beforehand, e.g., handwritten digits, or credit default risks.