But anyway. I'll probably do both anyway, because, of course, it is not yet perfectly democratic, and anyone arguing that it *is* democratic must concede that point.
The EU is a democracy in the following ways: it has a directly elected Parliament, whose approval is necessary for any legislation to pass. It has two separate bodies, the EU Council and Council of the EU, composed of elected representatives of the member states; the EU Council's approval is also needed for legislation to pass, and indeed currently most decisions require a supermajority (55% of states, representing 65% of the EU population) to be approved.
All of these give direct or indirect links to the democratic will of its constituent states and to its people.
The stumbling block is, as someone either soon will or already has pointed out while I'm typing this, the EU Commission, which is not elected, but is at least supervised by the Parliament, and whose members are selected by the governments of each member state. Still, that has powers that go beyond what a perfect democracy would allow. I believe the purpose is to ensure that legislation is proposed by disinterested officials, but ultimately still approved only by democratic bodies.
So, my answer is -- and has always been -- "yes, mostly". Like all democracies it has its flaws, but as long as the EU Parliament exists, and its role in particular has grown over time, then there is a clear democratic link.